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

Answer:

z(max)  =  5000

x₁  =  2

x₂  = 32

Step-by-step 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