Question

A surfboard manufacturer makes small and large surfboards. The production process has three stages: assembly, finish, and inspection. Each small surfboard requires 3 hours to assemble, 2 hours to finish, and 1 hour for inspection. Each large surfboard requires 4 hours to assemble, 3 hours to finish, and 1.5 hours for inspection. There are 140 hours available for assembly, 100 hours to finish, and 50 hours for inspection. The large surfboard makes $150 profit per board. The small surfboard makes $100 profit per board.Linear programming will be used to create the weekly production schedule.What would be a constraint for this problem if S

Answer 1

z(max) = 5000

x₁ = 2

x₂ = 32

Explanation:

Time Assemble Finish Inspection Profit

Small x₁ 3 2 1 100

Large x₂ 4 3 1,5 150

Availablity 140 100 50

Objective function:

z = 100*x₁ + 150*x₂ to maximize

Subject to:

First constraint assembly capacity 140 hours

3*x₁ + 4*x₂ ≤ 140

Second constraint finishing capacity 100 hours

2*x₁ + 3*x₂ ≤ 100

Third constraint inspection capacity 50 hours

x₁ + 1,5*x₂ ≤ 50

Model:

z = 100*x₁ + 150*x₂ to maximize

Subject to:

3*x₁ + 4*x₂ ≤ 140

2*x₁ + 3*x₂ ≤ 100

x₁ + 1,5*x₂ ≤ 50

General constraints x₁ ≥ 0 x₂ ≥ 0 and integers

With the use of AtomZmath.com (online solver)

After 6 iterations the solution is:

z(max) = 5000

x₁ = 2

x₂ = 32