A chain saw requires 7 hours of assembly and a wood chipper 3 hours. A maximum of 63 hours of assembly time is available. The profit of $190 on a chain saw and $220 on a chipper. How many of each should be assembled for maximum profit?

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  1. number of chain saws --- x
    number of chippers ----- y

    7x + 3y ≤ 63 ---> time inequation

    profit = 190x + 220y

    we need integer values of x and y
    only possible cases from 7x + 3y = 63 :
    (0,21) , (3,14), (6,7), (9,0)

    for (0,21) profit = 0 + 4620 = 4620
    for (3,14) profit = 570 + 3080 = 3650
    for (6,7) profit = 1140 + 1540 = 2680
    for (9,0) profit = 1710+0 =1710

    looks like they should make chippers only, they could make 21 of them for a profit of $4620.

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