Enrobe Textiles,Inc.,is a small clothing manufacturer that produces men's polo shirts and pants.The production manager,Zhang Wei,uses two primary resources: sewing machine hours and cutting machine hours.For next month's production of shirts and pants,Mr.Wei can schedule up to 300 hours of sewing machine time and up to 240 hours of cutting machine time.Production of each polo shirt requires 3.0 hours of sewing time and 1.0 hour of cutting time.Each pair of pants requires 2.0 hours of sewing time and 2.0 hours of cutting time.Based on the analysis of cost and sales figures,Mr.Wei estimates that each polo shirt will yield a profit of $5,and each pair of pants will generate a profit of $7.Given this scenario,what will be the maximum profits that Enrobe Textiles can achieve?
A)$525
B)$390
C)$450
D)$885

Question

Quizplus · Accepted Answer

Let x be the number of polo shirts produced and y be the number of pants produced. The objective is to maximize the profit,
Z = 5x + 7y
subject to the constraints,
3x + 2y ≤ 300 (sewing machine hours)
x + 2y ≤ 240 (cutting machine hours)
x, y ≥ 0 (non-negativity)
Graphing these constraints, we get a feasible region with vertices at (0,0), (0,120), (80,100), and (100,0).
Substituting these vertices into the objective function, we get the following values of Z:
(0,0): Z = 0
(0,120): Z = 840
(80,100): Z = 900
(100,0): Z = 500
Therefore, the maximum profit that Enrobe Textiles can achieve is $900 by producing 80 polo shirts and 100 pants. Answer: D.