Question

a Sewch yarap Titan Gop Nett termid-TS STUSESTUM Your answers are saved automatically Lol Rehbe: Oyuncu BestLeague W - YOUT Question Completion Status: Save and submit Click Submit to complete this assessment. Question 4 of 4 Question 4 30 points A company manufactures and sells two models of chairs, P1 and P2. The profits per unit of P1 and P2 are $55 and $80, respectively. Manufacturing one unit PI requires 70 minutes manual work and 20 minutes mechanical (machine) work. Manufacturing one unit P2 requires 90 minutes manual work and 40 minutes mechanical (machine) work. The manual work available per month is 6000 minutes and the machine is limited to only 4800 minutes per month. The manager wants to determine the number of P1 and P2 models to produce monthly to maximize profit. Formulate an integer LP model for this problem. (30 pts) TTT Arial • 3 (12) .T.EE Pathp Wordso 1605 HI E

Answer 1

The objective function is to maximize profit:

Z = 55 X1 + 80 X2

Subject to the constraints:

70 X1 + 90 X2 ≤ 6000 (manual work constraint)

20 X1 + 40 X2 ≤ 4800 (machine work constraint)

X1, X2 ≥ 0 (non-negativity constraints)

X1, X2 ∈ integers

Working Note:

1. For the objective function

Let the number of P1 chairs be = X1

Let the number of P2 chairs be = X2

The profit for 1 unit of P1 = $55

Total profit for 'X1' number of such chairs = 55 X1

The profit for 1 unit of P2 = $80

Total profit for 'X2' number of such chairs = 80 X2

Total combined profit = 55 X1 + 80 X2

2. For Manual work constraint

Manual work time required for 1 unit of P1 = 70 minutes

Total manual work time required for 'X1' number of units of P1 = 70 X1

Manual work time required for 1 unit of P2 = 90 minutes

Total manual work time required for 'X2' number of units of P2 = 90 X2

Total manual work time available = 6000 minutes

Total combined time required for P1 and P2 = 70 X1 + 90 X2

This total combined time would be less than or equal to the total available time, i.e., 6000 minutes

3. For Machine work constraint

Machine work time required for 1 unit of P1 = 20 minutes

Total Machine work time required for 'X1' number of units of P1 = 20 X1

Machine work time required for 1 unit of P2 = 40 minutes

Total Machine work time required for 'X2' number of units of P2 = 40 X2

Total Machine work time available = 4800 minutes

Total combined time required for P1 and P2 = 20 X1 + 40 X2

This total combined time would be less than or equal to the total available time, i.e., 4800 minutes