At one of its factories, a jeans manufacturer makes two styles: #891 and #917. Each pair of style-891 takes 10 minutes to cut out and 20 minutes to assemble and finish. Each pair of style-917 takes 10 minutes to cut out and 30 minutes to assemble and finish. The plant has enough workers to provide at most 7,500 minutes per day for cutting and at most 19,500 minutes per day for assembly and finishing. The profit on each pair of style-891 is $6.00 and the profit on each pair of style-917 is $8.50. How many pairs of each style should be produced per day to obtain maximum profit? Find the maximum daily profit. Round your profit to the nearest cent and anothet answers - to the nearest whole number.
A)350 pairs of style #891 and 400 pairs of style #917 for maximum profit of $5,500.00
B)300 pairs of style #891 and 450 pairs of style #917 for maximum profit of $5,625.00
C)299 pairs of style #891 and 399 pairs of style #917 for maximum profit of $5,185.50
D)225 pairs of style #891 and 375 pairs of style #917 for maximum profit of $4,537.50
E)310 pairs of style #891 and 300 pairs of style #917 for maximum profit of $4,410.00

Question

At one of its factories, a jeans manufacturer makes two styles: #891 and #917. Each pair of style-891 takes 10 minutes to cut out and 20 minutes to assemble and finish. Each pair of style-917 takes 10 minutes to cut out and 30 minutes to assemble and finish. The plant has enough workers to provide at most 7,500 minutes per day for cutting and at most 19,500 minutes per day for assembly and finishing. The profit on each pair of style-891 is $6.00 and the profit on each pair of style-917 is $8.50. How many pairs of each style should be produced per day to obtain maximum profit? Find the maximum daily profit. Round your profit to the nearest cent and anothet answers - to the nearest whole number. ​
A)350 pairs of style #891 and 400 pairs of style #917 for maximum profit of $5,500.00
B)​300 pairs of style #891 and 450 pairs of style #917 for maximum profit of $5,625.00
C)​299 pairs of style #891 and 399 pairs of style #917 for maximum profit of $5,185.50
D)​225 pairs of style #891 and 375 pairs of style #917 for maximum profit of $4,537.50
E)310 pairs of style #891 and 300 pairs of style #917 for maximum profit of $4,410.00

Quizplus · Accepted Answer

Let x be the number of pairs of style-891 and y be the number of pairs of style-917 produced per day.
The constraints are:
10x + 10y ≤ 7,500 (cutting time constraint)
20x + 30y ≤ 19,500 (assembly and finishing time constraint)
where all variables are non-negative integers.

The profit function is: P(x,y) = 6x + 8.5y

We can graph the feasible region and use the corner point method to find the maximum profit.

The feasible region is a polygon with vertices at:
(0,0), (300,450), (375,325), and (750,0)

We can evaluate the profit function at each corner point to find the maximum:
P(0,0) = $0
P(300,450) = $5,625.00
P(375,325) = $5,185.50
P(750,0) = $4,500.00

Therefore, the maximum profit is $5,625.00 and it occurs when the manufacturer produces 300 pairs of style-891 and 450 pairs of style-917 per day.

At One of Its Factories, a Jeans Manufacturer Makes Two