A bicycle builder makes two models. The basic model requires 2 hours of frame construction, 4 hours of assembly, and 1 hour of finishing. The deluxe model requires 3 hours of frame construction, 3 hours of assembly, and 2 hours of finishing. Each day 36 hours are available for frame construction, 40 hours for assembly, and 20 hours for finishing. If the profit on the basic model is $100 and on the deluxe model is $150, how many of each should be made to maximize the profit?

Question

Steve · Answer

If I do my math right, we have for b=basic and d=deluxe

construction: 2b+3d <= 36
assembly: 4b+3d <= 40
finishing: b + 2d <= 20

These graphs provide the intersection point b=8, d=4

so profit = 100b + 150d = 800 + 600 = 1400