Question

Billy Penny is trying to determine how many units of two types of cordless telephones to produce each day. One of these is the standard model, while the other is the deluxe model. The profit per unit on the standard model is $90, while the profit per unit on the deluxe model is $120. Each of these requires 30 minutes of assembly time, while the Deluxe model requires 35 minutes of assembly time. The Standard model requires 10 minutes of inspection time, while the Deluxe model requires 15 minutes of inspection time. The company must fill an order for 6 Deluxe models. There are 450 minutes of assembly time and 180 minutes of inspection time available each day.
Required:
Formulate as an LP, solve using QM, then interpret your output.

Answer 1

Answer:

The optimal solution is 3 standard telephones and 10 deluxe telephones for a maximum profit of $1,470.

Explanation:

we have to maximize profit following the equation 90s + 120d

the constraints are:

30s + 35d ≤ 450  

10s + 15d ≤ 180

d ≥ 6  

s ≥ 0

using solver, the optimal solution is 3 standard telephones and 10 deluxe telephones for a maximum profit of $1,470.

we can check our solution:

(90 x 3) + (120 x 10) = 1,470

(30 x 3) + (35 x 10) = 440 ≤ 450

(10 x 3) + (15 x 10) = 180 ≤ 180

10 ≥ 6  

3 ≥ 0