Question

Write the word or phrase that best completes each statement or answers the question. Solve the problem.

Two kinds of cargo, A and B, are to be shipped by truck. Each crate of cargo A is 50 cubic feet in volume and weighs 200 pounds, whereas each crate of cargo B is 10 cubic feet in volume and weighs 360 pounds. The shipping company charges $75 per crate for cargo A and $100 per crate for cargo B. The truck has a maximum load limit of 7200 pounds and 1000 cubic feet. How many crates of each cargo should be shipped on each truck in order to satisfy the load limits and yield the greatest charges? What is the greatest charge?

Answer 1

z(max) = 2350

x₁ = 18 x₂ = 10

Explanation:

Vol (ft³) W (p) Income ($)

Cargo A (x₁) 50 200 75

Cargo B (x₂) 10 360 100

Max load limit 1000 7200

Objective Function

z = 75*x₁ + 100*x₂

Constraints:

Volume constraint:

50*x₁ + 10*x₂ ≤ 1000

Weight constraint:

200*x₁ + 360*x₂ ≤ 7200

Model:

z = 75*x₁ + 100*x₂ to maximize

Subject to:

50*x₁ + 10*x₂ ≤ 1000

200*x₁ + 360*x₂ ≤ 7200

x₁ ≥ 0 x₂ ≥ 0 x₁ and x₂ integers

After 6 iterations with an on-line solver optimal solution is:

z(max) = 2350

x₁ = 18 x₂ = 10