Question

A company produces two types of jackets; windbreakers and rainbreakers. The company has at most 61 hours of finishing time per week and 67 hours of packaging time per week. Each windbreaker jacket takes 59 minutes of finishing time and 21 minutes of packaging time per week, whereas each rainbreaker jacket takes 58 minutes of finishing time and 34 minutes of packaging time per week. The company's profit for each windbreaker and rainbreaker jacket is 28 and 41, respectively. Let x denote the number of windbreaker jackets they should produce and y denote the number of rainbreaker jackets they should produce. The company wants to maximize profit. Set up the Linear Programming Problem for this situation.

Answer 1

Answer:

Max p = 28x + 41y

Subject to

59x + 58y ≤ 3660

21x + 34y ≤ 4020

x  ≥  0, y ≥ 0

Step-by-step explanation:

As given ,

                                       Windbreakers          Rain breakers              Total

Finishing time                         59 min                     58 min                   61 hr

Packaging time                        21 min                      34 min                   68 hr

Profit                                          28                                41

Let

The number of windbreaker jackets they should produce = x

The number of rain breaker jackets they should produce = y

As given,

The company wants to maximize profit.

⇒ Maximum Profit , p = 28x + 41 y

Now,

As 1 hour = 60 min

⇒61 hours = 61×60 = 3660 min

and 67 hours = 67×60 = 4020 min

∴ we get

The equations become

59x + 58y ≤ 3660

21x + 34y ≤ 4020

x  ≥  0, y ≥ 0

So, the Linear Programming Problem (LPP) for this problem is -

Max p = 28x + 41y

Subject to

59x + 58y ≤ 3660

21x + 34y ≤ 4020

x  ≥  0, y ≥ 0