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Can you help me with this linear programming question ?
(a)Budget Airlines is considering setting up an air service based at Exeter International Airport. Initially it has two destinations in mind: La Rochelle, France and Reus, Spain. The airline has one gate at Exeter Airport which operates 12 hours per day. Each flight requires 1 hour of gate time. Each flight to Reus consumes 15 hours of pilot crew time and is expected to produce a profit of 2,500 €. Serving La Rochelle uses 10 hours of pilot crew time per flight and will result in a profit of 2,000€. Pilot crew labour is limited to 150 hours per day. The market for flights to Reus is limited to nine flights per day.
Determine the most profitable number of flights to operate on a daily basis and hence the maximum daily profit.
1 Antwort
- Kathleen KLv 7vor 8 JahrenBeste Antwort
Let x = the number of flights to La Rochelle
Let y = the number of flights to Reus
Constraints:
x+y ≤ 12
10x + 15y ≤ 150
0 ≤ y ≤ 9
x ≥ 0 ← assumed
Objective:
Maximize P(x,y) = 2000x + 2500y
When you graph the system of inequalities, you get a pentagonal "feasible region" with these vertices:
(0,0)
(0,9)
(3,9)
(6,6)
(12,0)
Some of those vertices are clear from the region, and a couple do require a quick system of equations to find points of intersection. Basic algebra though.
Finally, you plug in all the vertices into the objective function and see which yields the maximum. In this case the maximum profit is €28500 at the point (3,9).
