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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.
and the intersection of the two lines,
Multiply eq. 1 by (-2) and eq. 2 by (3) and add them,
Then from eq. 1,
Check the profit function at each of the vertices.
The max and min will occur at one of these points.
Maximum profit is $45,000 and occurs when you make 900 of Product A and 0 of Product B.