# Fast Co. is a delivery company based in Minneapolis, MN. Jet fuel is one of the most significant…

Fast Co. is a delivery company based in Minneapolis, MN. Jet fuel is one of the most significant costs incurred by the company, and they want assistance in managing this cost. The price of fuel varies at airports around the country. Thus, it might be wise to fill up on fuel at airports where it is cheapest. However, the amount of fuel a plane burns partly depends on the plane’s weight – and excess fuel makes an plane heavier and, therefore, less fuel-efficient. The table shows the flight schedule flown nightly. For each flight, the table summarizes the minimum required and maximum allowable amount of fuel onboard at takeoff and the fuel cost at each point of departure. The final column provides a linear function relating fuel consumption to the amount of fuel onboard at takeoff.

For example, if the plane leaves Minneapolis for Chicago with 25,000 gallons on board, it should arrive in Chicago with approximately 25,000 – (2100 + 0.7 x 25000) = 5,400 gallons.

The company wants to create a Linear Programming model to find the schedule’s most economical fuel purchasing plan.

Hint: The most fuel you would purchase at any departure point is the maximum allowable fuel level for takeoff at that point. Assume that whatever fuel is on board when the plane returns to Minneapolis at the end of the rotation will still be on board when the plane leaves Minneapolis the following evening.

1. Define the decision variables, objective function, and constraints.
2. How much fuel should the US Express purchase at each departure point, and what is the cost of this purchasing plan?

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