Question

food and clothing, are shipped to victims of a natural disaster, each carton of food will feed 14 people, while, each carton of clothing will help 6 people. Each 25 ft.³ box of food weighs 50 pounds and each 5 ft.³ box of clothing weighs 20 pounds. The commercial carries transporting food and clothing are bound by the following constraints. The total weight per carrier cannot exceed 23,000 pounds the total volume must be no more than 8000 ft.³ use this information to answer the following questions how many cartons of food and clothing should be sent with each plane shipment to maximize the number of people who can be helped?

Answer 1

To maximize the number of people helped, we should send 180 cartons of food and 700 cartons of clothing

How many cartons of food and clothing should be sent with each plane

To maximize the number of people helped, we need to determine the optimal combination of food and clothing cartons within the given weight and volume constraints.

Let

• x represent the number of cartons of food and
• y represent the number of cartons of clothing.

So, the objective function is

Max Z = 14x + 6y

Subject to

50x + 20y ≤ 23,000

25x + 5y ≤ 8,000

Using the graphical method of linear programming, we find that the optimal solution is:

x = 180 cartons of food

y = 700 cartons of clothing

This means that to maximize the number of people helped, we should send 180 cartons of food and 700 cartons of clothing