HomeSearch by dateVacation packagesHotelsFlight dealsCar rentalTravel tips & news
Philadelphia

$54+ Cheap flights from West Palm Beach to Philadelphia (PBI - PHL)

This is the cheapest one-way flight price found by a Cheapflights user in the last 72 hours by searching for a flight departing on 12/11. Fares are subject to change and may not be available on all flights or dates of travel.
PBI — PHL
Dec 13 — Dec 201
Sat 12/13
Sat 12/20
1 adult, Economy
We work with more than 300 partners to bring you better travel deals

Find cheap flights from West Palm Beach to Philadelphia with Cheapflights

1. Tell us where you want to go

Enter your travel information like dates, passengers, trip type (one-way or round trip), and preferred cabin class then click “Find deals”

2. Select your favorite providers

We find the providers serving your travel needs. Choose up to four travel providers to compare side-by-side for flights, hotels, or car rentals.

3. Compare prices and book

Review each provider’s pricing and select the best option for you! Book through your favorite provider’s website for a seamless experience.

Cheapflights Tip: The best prices from Palm Beach Intl to Philadelphia are usually found in January or February, booked 68 days in advance, depart on a Thursday or Friday and return on a Tuesday

Find flight deals from West Palm Beach to Philadelphia

Cheapest flights from West Palm Beach to Philadelphia
Explore the most affordable flight options available from West Palm Beach to Philadelphia. Find the lowest fares from popular airlines and budget airlines, with prices last updated on November 13, 2025.

This Frontier deal was found by Cheapflights users on 11/12. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Frontier is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Thu 12/45:57 pmPBI - PHL
1 stop6h 54mFrontier
Sun 12/75:30 pmPHL - PBI
Nonstop2h 53mFrontier
Deal found 11/12$130
This Frontier deal was found by Cheapflights users on 11/12. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Frontier is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Thu 12/45:57 pmPBI - PHL
1 stop6h 54mFrontier
Sat 12/65:30 pmPHL - PBI
Nonstop2h 53mFrontier
Deal found 11/12$131
This Expedia deal was found by Cheapflights users on 11/11. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Expedia is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Fri 12/59:18 pmPBI - PHL
Nonstop2h 40mFrontier
Sun 12/75:30 amPHL - PBI
1 stop12h 29mFrontier
Deal found 11/11$133
This Priceline deal was found by Cheapflights users on 11/12. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Priceline is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Fri 12/59:18 pmPBI - PHL
Nonstop2h 40mFrontier
Mon 12/85:30 pmPHL - PBI
Nonstop2h 53mFrontier
Deal found 11/12$134
This Kiwi.com deal was found by Cheapflights users on 11/11. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Kiwi.com is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Sun 12/218:39 pmPBI - PHL
2 stops35h 58mMultiple Airlines
Sun 1/48:30 amPHL - PBI
Nonstop2h 58mMultiple Airlines
Deal found 11/11$136
This Super.com deal was found by Cheapflights users on 11/12. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Super.com is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Tue 12/910:12 amPBI - PHL
Nonstop2h 44mFrontier
Fri 12/125:30 pmPHL - PBI
Nonstop2h 53mFrontier
Deal found 11/12$137
This CheapOair deal was found by Cheapflights users on 11/11. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure CheapOair is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Sun 12/710:12 amPBI - PHL
Nonstop2h 44mFrontier
Tue 12/95:30 pmPHL - PBI
Nonstop2h 53mFrontier
Deal found 11/11$140
This Priceline deal was found by Cheapflights users on 11/11. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Priceline is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Sun 12/219:51 amPBI - PHL
Nonstop2h 39mFrontier
Sun 1/48:30 amPHL - PBI
Nonstop2h 58mFrontier
Deal found 11/11$142
This Frontier deal was found by Cheapflights users on 11/12. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure Frontier is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Wed 11/2612:45 pmPBI - PHL
Nonstop2h 43mFrontier
Wed 11/267:56 pmPHL - PBI
2 stops19h 02mFrontier
Deal found 11/12$144
This CheapOair deal was found by Cheapflights users on 11/12. Clicking the “Pick Dates” button in this card will allow you to select your dates and further customize your flight criteria. From there, click “Find deals”, make sure CheapOair is selected, and click “Compare selected” under the list of providers to see comparable flight deals.
Sat 12/610:12 amPBI - PHL
Nonstop2h 44mFrontier
Sun 12/75:30 amPHL - PBI
1 stop12h 29mFrontier
Deal found 11/12$145

Cheap flight deals from West Palm Beach to Philadelphia

Discover tips and strategies to find the most affordable flight options for your journey from West Palm Beach (PBI) to Philadelphia (PHL). Learn about various techniques such as flexible date searches, comparing prices across and setting up price alerts. Use these methods to find the cheapest flights available for your travel needs. Data last updated November 13, 2025.

Most accurate provider

CheapOair
3 stars

Most trusted provider

CheapOair
3 stars

Round-trip from

$130
(Frontier)

One-way from

$54
(Kiwi.com)

Popular in

September

Cheapest in

January

Average price

$274

Good round-trip deal

$202 or less

Good one-way deal

$137 or less
Provider with most accurate pricing for Palm Beach Intl-Philadelphia flight deals.
Search Deals
Provider most trusted by Cheapflights users for Palm Beach Intl-Philadelphia flights.
Search Deals
From Palm Beach Intl to Philadelphia
Search Deals
One-way flight from Palm Beach Intl to Philadelphia
Search Deals
Highest demand for flights based on searches. 17% potential increase in price ($51 potential increase over avg. RT price).
Search Deals
Cheapest flight prices on average. 3% potential price decrease ($9 potential savings vs. average RT price).
Search Deals
Average for round-trip flights in November 2025
Search Deals
Price to beat on a round-trip flight from Palm Beach Intl to Philadelphia.
Search Deals
Price to beat on a one-way flight from Palm Beach Intl to Philadelphia.
Search Deals

Cheapflights Fare Finder

 
Customize your flight search to find flights from West Palm Beach to Philadelphia that fit within your specific budget. Explore options based on user searches and filter the results based on your desired price range. Find flights that match your budget for a cost-effective journey. Over the last 7 days, Cheapflights users made 2,558,603 searches. Data last updated November 13, 2025.
Use the filters below to find and compare flights from West Palm Beach to Philadelphia that are best for you.

Fly from

West Palm Beach

Fly to

Philadelphia

Route

Depart

Return

Price

West Palm BeachPhiladelphia

PBI - PHL

PBIPHL

Palm Beach Intl

Sat 2/21

7:04 pm-9:46 pm

Nonstop2h 42m

Philadelphia

Mon 3/2

5:30 am-12:41 pm

1 stop7h 11m

$149

West Palm BeachPhiladelphia

PBI - PHL

PBIPHL

Palm Beach Intl

Sat 2/21

3:45 pm-10:03 pm

1 stop6h 18m

Philadelphia

Sat 2/28

6:55 am-1:09 pm

1 stop6h 14m

$199

West Palm BeachPhiladelphia

PBI - PHL

PBIPHL

Palm Beach Intl

Fri 2/20

6:11 pm-12:28 am

1 stop6h 17m

Philadelphia

Sun 3/1

6:55 am-1:09 pm

1 stop6h 14m

$199

West Palm BeachPhiladelphia

PBI - PHL

PBIPHL

Palm Beach Intl

Wed 2/18

8:00 am-1:24 pm

1 stop5h 24m

Philadelphia

Tue 2/24

6:55 am-1:09 pm

1 stop6h 14m

$199

West Palm BeachPhiladelphia

PBI - PHL

PBIPHL

Palm Beach Intl

Fri 1/16

6:11 pm-12:23 am

1 stop6h 12m

Philadelphia

Mon 1/19

5:40 am-11:40 am

1 stop6h 00m

$199

West Palm BeachPhiladelphia

PBI - PHL

PBIPHL

Palm Beach Intl

Thu 2/19

6:00 am-11:11 am

1 stop5h 11m

Philadelphia

Sat 2/28

6:55 am-2:40 pm

1 stop7h 45m

$199

West Palm BeachPhiladelphia

PBI - PHL

PBIPHL

Palm Beach Intl

Tue 2/17

6:11 pm-12:28 am

1 stop6h 17m

Philadelphia

Mon 3/2

6:55 am-1:09 pm

1 stop6h 14m

$199

West Palm BeachPhiladelphia

PBI - PHL

PBIPHL

Palm Beach Intl

Thu 1/15

6:11 pm-12:23 am

1 stop6h 12m

Philadelphia

Mon 1/19

5:40 am-11:40 am

1 stop6h 00m

$199

West Palm BeachPhiladelphia

PBI - PHL

PBIPHL

Palm Beach Intl

Thu 2/19

7:45 pm-12:28 am

1 stop4h 43m

Philadelphia

Mon 3/2

4:59 pm-12:16 am

1 stop7h 17m

$199

West Palm BeachPhiladelphia

PBI - PHL

PBIPHL

Palm Beach Intl

Sat 2/21

3:45 pm-10:03 pm

1 stop6h 18m

Philadelphia

Tue 2/24

6:55 am-1:09 pm

1 stop6h 14m

$199

Flights are sorted by cheapest round-trip flights first.

Deals found on 11/12

Showing 1-10 of 24 results
1
2
3

Compare providers for flights from West Palm Beach to Philadelphia

Provider information is updated monthly. Please note that these providers often have deals for this flight, but the availability may vary on a day-by-day basis on Cheapflights.
Use the table below to compare price accuracy, trust ratings, and cancellation policies for each provider offering flight deals from West Palm Beach to Philadelphia in November.
ProviderPrice AccuracyTrust Score*
ExpediaPrice Accuracy2 starsTrust Score*3 stars
FlightHubPrice Accuracy3 starsTrust Score*1 star
eDreamsPrice Accuracy3 starsTrust Score*3 stars
CheapflightsfaresPrice Accuracy3 starsTrust Score*2 stars
CheapOairPrice Accuracy3 starsTrust Score*3 stars
PricelinePrice Accuracy1 starTrust Score*3 stars

*The Trust Score is based on feedback from users after their booking experience. It measures overall satisfaction, helping us identify issues like hidden fees, problems during the ticketing process, and the quality of customer service. This score is our best indicator of the provider's quality and reliability.

  • Most accurate provider: When it comes to deals on West Palm Beach-Philadelphia flights, users find the pricing of CheapOair to be most consistent on Cheapflights vs. CheapOair Users can find the same prices on West Palm Beach-Philadelphia flight deals on Cheapflights vs. CheapOair >95% of the time. Price accuracy is based on data collected from West Palm Beach-Philadelphia flight searches over the past month and is updated monthly.
  • Most trusted provider: When it comes to deals on West Palm Beach-Philadelphia flights, Cheapflights users trust CheapOair the most. CheapOair has received a user feedback score of 3 out of 3 stars (3 being the best), meaning they have been trusted the most by Cheapflights users looking for West Palm Beach-Philadelphia flight deals. Provider user feedback score is based on Cheapflights searches over the past month and is updated monthly.

Best time to book a flight from West Palm Beach to Philadelphia

Have a flexible travel schedule? Discover the best time to fly to Philadelphia from West Palm Beach with our price prediction graph.
Estimated round-trip price
Rates are based on past data. Find the cheapest month and day to book your flight based on your travel requirements, then search for cheap deals.

Cheapflights Insights

Everything you need to know about your flight from West Palm Beach to Philadelphia

How far ahead should I book a flight from West Palm Beach to Philadelphia?

Use this chart to determine the optimal time to book a round-trip flight from West Palm Beach to Philadelphia. Price data was last updated on November 7, 2025.

Booking 68 days in advance of your planned departure date is, on average, the best time to get cheap flights from West Palm Beach to Philadelphia. The general trend is that the closer you book to the departure date, the more expensive your flight will be.

What is the cheapest month to book a flight from West Palm Beach to Philadelphia?

Currently, March is the cheapest month in which you can book a flight from West Palm Beach to Philadelphia (average of $40). Flying from West Palm Beach to Philadelphia in August is currently the most expensive (average of $73). There are several factors that can impact the price of a flight, so comparing airlines, departure airports and flight times can provide users with more options.

What is the cheapest time of day to fly from PBI to PHL?

Find hourly flight availability from West Palm Beach to Philadelphia. Discover flight options and departure times throughout the day, allowing you to choose a departure time that suits your schedule. Data last updated November 13, 2025.

Unlike at noon, when flights are generally more expensive, you can save up to 64% on flights from West Palm Beach to Philadelphia by exploring options for tickets in the evening.

What is the cheapest day to fly from West Palm Beach to Philadelphia?

Use this chart to determine the cheapest time to fly round-trip from West Palm Beach to Philadelphia. Price data was last updated on November 2, 2025.

Travelers seeking maximum savings on their West Palm Beach to Philadelphia flight should consider departing on Tuesday evenings when fares are most often at their lowest. Sunday afternoons flights should be avoided if possible as fares are typically the most expensive at this time.

The best insider tips for West Palm Beach to Philadelphia flights

Snippets provided in this section are AI-generated based on a summarization of Cheapflights-commissioned articles. The articles are presented as-is, for general informational purposes only, and may not be up-to-date. The opinions contained in the articles are original to the author and reflect their authentic experience, which may vary significantly from the experience of others.
Cheapflights partnered with top experts to bring you the best recommendations for your West Palm Beach to Philadelphia trip
Airports
PBI

PBI's easy-to-navigate terminal features a landside shopping and dining area with natural light and cushioned seating, perfect for relaxing before your flight.

Read more about PBIby Ramsey Qubein
PHL

For a quick trip to Center City, SEPTA trains are the most efficient option, with stations conveniently located outside Terminals A, B, C/D, and E/F.

Read more about PHLby Mark Chesnut
Our travel experts
Mark Chesnut

Mark Chesnut

Expert on PHL

Mark Chesnut

Mark Chesnut

Mark Chesnut is a travel writer and public speaker with more than 30 years of experience. The 2019 winner of the NLGJA Excellence in Travel Writing Award, Mark is the author of the book “Prepare for Departure” and has covered air travel for multiple top consumer and trade media outlets.

Read more
Ramsey Qubein

Ramsey Qubein

Expert on PBI

Ramsey Qubein

Ramsey Qubein

An avid traveler and aviation expert who has visited 173 countries, all 50 states and seven continents, Ramsey Qubein flies nearly 400,000 miles a year. As a North Carolina-based freelance journalist for publications including Conde Nast Traveler, Forbes, USA Today and Bloomberg among others, he explores the latest trends in aviation, hospitality, cruises and business.

Read more

Reviews of airlines servicing Philadelphia

Get insights into the airlines that provide service to Philadelphia. Read reviews, discover amenities, and learn about the overall travel experience offered by airlines. Use this information to make informed decisions when choosing an airline for your flight to Philadelphia. Reviews last updated November 13, 2025.
Get a feel of what it's like to fly with American Airlines, JetBlue, and Spirit Airlines from West Palm Beach to Philadelphia by reading reviews from past customers. Users have also rated airlines in terms of entertainment options, comfort, food, crew/service, and boarding process.
American Airlines
7.2
Good
11,051 reviews

Crew

8.0

Overall

7.2

Food

6.4

Comfort

7.2

Boarding

7.5

Entertainment

6.9

Reviews

1 / 20
2.0
Mediocre

Jeremy,Sep 2025

SAN - PHL

Terrible. Bad customer service and unacceptable delay on the tarmac
American Airlines
7.2
Good
11,051 reviews
American Airlines
7.2
Good
11,051 reviews

Crew

8.0

Overall

7.2

Food

6.4

Comfort

7.2

Boarding

7.5

Entertainment

6.9

Reviews

1 / 20
2.0
Mediocre

Jeremy,Sep 2025

SAN - PHL

Terrible. Bad customer service and unacceptable delay on the tarmac
JetBlue
7.2
Good
2,907 reviews
American Airlines
7.2
Good
11,051 reviews

Crew

8.0

Overall

7.2

Food

6.4

Comfort

7.2

Boarding

7.5

Entertainment

6.9

Reviews

1 / 20
2.0
Mediocre

Jeremy,Sep 2025

SAN - PHL

Terrible. Bad customer service and unacceptable delay on the tarmac
Spirit Airlines
6.3
Okay
8,139 reviews
American Airlines
7.2
Good
11,051 reviews

Crew

8.0

Overall

7.2

Food

6.4

Comfort

7.2

Boarding

7.5

Entertainment

6.9

Reviews

1 / 20
2.0
Mediocre

Jeremy,Sep 2025

SAN - PHL

Terrible. Bad customer service and unacceptable delay on the tarmac
Frontier
5.8
Fair
3,109 reviews
American Airlines
7.2
Good
11,051 reviews

Crew

8.0

Overall

7.2

Food

6.4

Comfort

7.2

Boarding

7.5

Entertainment

6.9

Reviews

1 / 20
2.0
Mediocre

Jeremy,Sep 2025

SAN - PHL

Terrible. Bad customer service and unacceptable delay on the tarmac

Related info for your journey

Find useful and relevant information for your journey from West Palm Beach to Philadelphia. Access travel guides, tips, and recommendations to enhance your travel experience. Get information about local attractions, weather, transportation options, and more.

  • What airports do I use to fly from West Palm Beach to Philadelphia?

    If you book a flight from West Palm Beach to Philadelphia, you will be flying from Palm Beach Intl to Philadelphia. Flights to Philadelphia (PHL) from Palm Beach Intl (PBI) take 2h 39m for a nonstop flight. There are 4 flights from Palm Beach Intl to Philadelphia per day from 4 airlines.

  • How popular is this West Palm Beach to Philadelphia flight route?

    Within the past month, 17 users have taken a look at flights from Palm Beach Intl to Philadelphia.

  • How long is the flight from West Palm Beach to Philadelphia?

    For as low as $149, Frontier can have you in Philadelphia from West Palm Beach in 2h 42m. Airlines will cover a distance of 953 mi. Both multi-stop and nonstop flights can be found to your destination and back.

  • What are the cheapest airlines flying from West Palm Beach to Philadelphia round-trip?

    Cheapflights users have booked flights from West Palm Beach to Philadelphia round-trip from $38. Other airlines that can offer you cheap pricing are Frontier, from $76, and JetBlue, from $141. Users have found that Spirit Airlines is 84% cheaper than the other options available to this destination.

  • What are the most reliable airlines from West Palm Beach to Philadelphia?

    The top 3 most reliable airlines when flying from West Palm Beach to Philadelphia are Frontier (89%), Qatar Airways (79%) and British Airways (77%).

  • What are the cheapest flights from West Palm Beach to Philadelphia?

    Looking at all options, your cheapest flight can be booked for $76. While the most popular route (Palm Beach Intl - Philadelphia) can be booked for $65 on average, our data indicates $269 when flying from West Palm Beach to Philadelphia.

  • Can I find deals for flights from West Palm Beach to Philadelphia that include hotel bookings?

    Yes. In addition to deals on West Palm Beach to Philadelphia flights, Cheapflights offers vacation packages that include both flights and hotel.

  • How can I find direct flights from West Palm Beach to Philadelphia?

    After entering your origin and destination, apply the non-stop filter on the search result page to find direct flights from West Palm Beach to Philadelphia.

  • Can I find deals for business class flights from West Palm Beach to Philadelphia?

    Yes. Cheapflights offers flight deals from West Palm Beach to Philadelphia by cabin class. In addition to browsing deals, you can also filter by cabin class on the search results page after making a search.

  • What is the cheapest month to book a flight from West Palm Beach to Philadelphia?

    Currently, March is the cheapest month in which you can book a flight from West Palm Beach to Philadelphia (average of $40). Flying from West Palm Beach to Philadelphia in August is currently the most expensive (average of $73). There are several factors that can impact the price of a flight, so comparing airlines, departure airports and flight times can provide users with more options.

See more FAQs

Traveling to a place near Philadelphia?

Book flights to Philadelphia if you plan to visit one of these locations
Wildwood
King of Prussia
Pottstown
Reading
Ocean City
Cherry Hill
Dewey Beach
Ephrata
Camden
Vineland
Milford
Dover
Elkton
Essington
Willow Grove
New Castle
Newark
Millville
Chester
Exton

Browse thousands of different options on Cheapflights for your next trip

Toggle through the tabs below to find thousands of options on Cheapflights for your next trip.

Alternative routes for West Palm Beach to Philadelphia

See prices for flight routes from nearby airports that may be better suited for you.
Fort Lauderdale to John F Kennedy Intl flights
Miami to John F Kennedy Intl flights
Fort Lauderdale to LaGuardia flights
Orlando to John F Kennedy Intl flights
Fort Lauderdale to Newark flights
Tampa to John F Kennedy Intl flights
Tampa to LaGuardia flights
Tampa to Newark flights
Orlando to LaGuardia flights
Miami to LaGuardia flights
Miami to Newark flights
Orlando to Newark flights
West Palm Beach to John F Kennedy Intl flights
West Palm Beach to Newark flights
West Palm Beach to LaGuardia flights
Jacksonville to John F Kennedy Intl flights
Jacksonville to LaGuardia flights
Tampa to Dulles Intl flights
Jacksonville to Newark flights
Orlando to Dulles Intl flights
Orlando to Reagan-National flights
Miami to Reagan-National flights
Miami to Dulles Intl flights
Orlando to Philadelphia flights
Fort Myers to John F Kennedy Intl flights
Tampa to Philadelphia flights
Fort Lauderdale to Philadelphia flights
Fort Myers to LaGuardia flights
Tampa to Reagan-National flights
Fort Lauderdale to Reagan-National flights
Fort Myers to Newark flights
Fort Lauderdale to Dulles Intl flights
Sarasota to Newark flights
Jacksonville to Dulles Intl flights
Sarasota to John F Kennedy Intl flights
Miami to Philadelphia flights
West Palm Beach to Reagan-National flights
Jacksonville to Philadelphia flights
Jacksonville to Reagan-National flights
Orlando to Pittsburgh flights
Pensacola to LaGuardia flights
Fort Myers to Philadelphia flights
West Palm Beach to Dulles Intl flights
Fort Myers to Reagan-National flights
Fort Myers to Dulles Intl flights
Tampa to Pittsburgh flights
Sarasota to LaGuardia flights
Panama City to LaGuardia flights
Daytona Beach to John F Kennedy Intl flights

Top 4 airlines flying from West Palm Beach to Philadelphia

Discover the top 4 airlines that operate flights from West Palm Beach to Philadelphia. Compare their services, reliability, and customer satisfaction ratings to choose the airline that best suits your travel preferences and needs. Over the last 7 days, Cheapflights users made 2,558,603 searches. Data last updated November 13, 2025.
AirlineCheapestAverageFlexibilityOn-time
Spirit AirlinesCheapest$38Average$144FlexibilityNo cancel feeOn-time65%
FrontierCheapest$76Average$162FlexibilityNo cancel feeOn-time62%
JetBlueCheapest$141Average$207FlexibilityNo cancel feeOn-time62%
American AirlinesCheapest$178Average$326FlexibilityNo cancel feeOn-time71%

100% Free

Cheapflights is completely free to use, so you can start saving the moment you arrive.

Book with Flexibility

Our users can plan ahead with confidence and find flights with no change fees

Travel Smart

Millions of people come to us for their flight needs every year. We help make travel planning easy by providing useful insights and data-driven graphs that can inform your decisions.