A humanitarian agency can use two models of vehicles for a refugee rescue mission.Each model A vehicle costs $1000 and each model B vehicle costs $1500.Mission strategies and objectives indicate the following constraints. A total of at least 20 vehicles must be used.
A model A vehicle can hold 45 boxes of supplies.A model B vehicle can hold 30 boxes of supplies.The agency must deliver at least 690 boxes of supplies to the refugee camp.
A model A vehicle can hold 20 refugees.A model B vehicle can hold 32 refugees.The agency must rescue at least 520 refugees.
What is the optimal number of vehicles of each model that should be used? What is the optimal cost?
A) A minimum cost of $27,000 occurs when 6 vehicles of each model are used.
B) A minimum cost of $27,000 occurs when 14 vehicles of each model are used.
C) A minimum cost of $34,500 occurs when 23 vehicles of each model are used.
D) A minimum cost of $26,000 occurs when 26 vehicles of each model are used.
E) A minimum cost of $25,000 occurs when 10 vehicles of each model are used.

Question

Quizplus · Accepted Answer

We can use linear programming to find the optimal solution to this problem. Let x be the number of model A vehicles and y be the number of model B vehicles.

Objective function:
Minimize cost = 1000x + 1500y

Constraints:
x + y ≥ 20 (total of at least 20 vehicles)
45x + 30y ≥ 690 (deliver at least 690 boxes of supplies)
20x + 32y ≥ 520 (rescue at least 520 refugees)

Solving the linear program using a software program or calculator, we get the optimal solution of x = 10 and y = 10. This means that 10 model A vehicles and 10 model B vehicles should be used for the mission. The total cost is 10(1000) + 10(1500) = $25,000, which is the minimum cost that can be achieved while still meeting all the mission constraints. Therefore, the best choice is E.

A Humanitarian Agency Can Use Two Models of Vehicles for a Refugee