Question 316557: DUchess Blue Corporation wants to maximize its profit on products A and B. The profit on one unit of Produc A is $50, while the profit on one unit of Product B is $45. Each unit of Product A requires 3 hours of assembly time and 2 hours of finishing time, while each unit of Product B requires 4 hours of assembly time and 6 hours of finishing time. The departmental capacity (in total hours) is 2700 for assembly and 2400 for finishing. What is the maximum profit, and how many of each product should be produced in order to achieve that profit?
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! Let x be the number of Product A.
Let y be the number of Product B.
The profit is then
with the constraints that,
Assembly Time Total
Finishing Time Total
Plot all of the constraints to find the feasible region.
Find the intersection points.
(0,0)
(0,400)
(900,0)
and the intersection of the two lines,
1.
2.
Multiply eq. 1 by (-2) and eq. 2 by (3) and add them,
Then from eq. 1,
.
.
.
(660,180)
.
.
.
Check the profit function at each of the vertices.
The max and min will occur at one of these points.
(0,0):
(0,400):
(900,0):
(660,180):
.
.
.
Maximum profit is $45,000 and occurs when you make 900 of Product A and 0 of Product B.
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