What are the constraints?
Suppose you own an airline which operates two types of flights – Pittsburgh to Boston and Pittsburgh to Phoenix. A flight to Boston earns your company $5,000 profit and a flight to Phoenix earns your company $9,000 profit. You have 8 planes available, and in a given day a plane can make one flight to Phoenix or two flights to Boston. You have ten pilot crews available, and a crew may only make one flight per day regardless of length. Write a linear programming problem to maximize profit. I understand how to set up a simplex tableau and go about solving for the best possible objective, but i cant figure out the constraints from the wording of this problem.
Mathematics - 1 Answers
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Fun! Let: x be flights to Phoenix y be flights to Boston max z = 9x + 5y x + 0.5y <= 8 x + y <= 10 But this should make sense since one plane can make two flights to Boston, so for example: x = 2, y = 8 means 2 planes go to Phoenix, 4 planes go to Bostom, 2+0.5*8 = 6 <= 8 2 crew go to Phoenix, 8 crew go to Boston. 2 + 8 = 10
