Questions: Answer the following questions based on the given scenario: Gentleman's Attire Company produces quality men's suits. One suit consists of a jacket and pants. The profit on a pair of pants is 2, and 1.50 on a jacket. Both pants and jackets require the work of sewing operators and cutters. It takes 8 minutes to sew one pair of pants and 4 minutes to cut. It takes 4 minutes to sew one jacket and 8 minutes to cut. There are 60 minutes of sewing time and 48 minutes of cutter time available. Gentleman's Attire Company's goal is to maximize its profits. Let x = number of pants and y = number of jackets. Fill in the blank. The maximum profit is

Answer the following questions based on the given scenario: Gentleman's Attire Company produces quality men's suits. One suit consists of a jacket and pants. The profit on a pair of pants is 2, and 1.50 on a jacket. Both pants and jackets require the work of sewing operators and cutters. It takes 8 minutes to sew one pair of pants and 4 minutes to cut. It takes 4 minutes to sew one jacket and 8 minutes to cut. There are 60 minutes of sewing time and 48 minutes of cutter time available. Gentleman's Attire Company's goal is to maximize its profits. Let x = number of pants and y = number of jackets. Fill in the blank. The maximum profit is
Transcript text: Answer the following questions based on the given scenario: Gentleman's Attire Company produces quality men's suits. One suit consists of a jacket and pants. The profit on a pair of pants is $2, and $1.50 on a jacket. Both pants and jackets require the work of sewing operators and cutters. It takes 8 minutes to sew one pair of pants and 4 minutes to cut. It takes 4 minutes to sew one jacket and 8 minutes to cut. There are 60 minutes of sewing time and 48 minutes of cutter time available. Gentleman's Attire Company's goal is to maximize its profits. Let $x$ = number of pants and $y$ = number of jackets. Fill in the blank. The maximum profit is \$ $\qquad$
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Solution

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Solution Steps

Step 1: Formulate the objective function

The objective is to maximize profit. Profit is $2 per pair of pants (x) and $1.50 per jacket (y). So the objective function is: Profit = 2x + 1.5y

Step 2: Formulate the constraints
  • Sewing constraint: 8x + 4y ≤ 60
  • Cutting constraint: 4x + 8y ≤ 48
Step 3: Find the feasible region and corner points

The constraints can be simplified:

  • Sewing: 2x + y ≤ 15
  • Cutting: x + 2y ≤ 12

Corner points are where the constraint lines intersect or intersect with the axes (x≥0, y≥0).

  • (0,0): Profit = 2(0) + 1.5(0) = $0
  • (0,6): Profit = 2(0) + 1.5(6) = $9
  • (7.5, 0): Profit = 2(7.5) + 1.5(0) = $15
  • Intersection of 2x + y = 15 and x + 2y = 12: Solving this system yields x = 6 and y = 3. Profit = 2(6) + 1.5(3) = $16.50

Final Answer

16.5

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