SOLUTION: 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

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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.