Math

A print manufacturer makes two types of printers: a Printmaster and Speedmaster. The Printmaster requires 10 cubic feet of space and weighs 5,000 pounds, and the Speedmaster takes up 5 cubic feet of space and weighs 600 pounds. The total available space for storage before shipping is 2,000 cubic feet, and the weight limit for the space is 300,000 pounds. The profit on the Printmaster is $125,000, and the profit on the Speedmaster is $30,000. How many of each machine should be stored to maximize profitability, and what is the maximum possible profit?

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  1. p = number of printmasters
    s = number of speedmasters

    (1) vol = 10 p + 5 s < 2000

    (2) wt = 5000 p + 600 s < 300000

    maximize
    gain = g = 125000 p + 30000 s

    p on x axis , s on y axis
    do quadrant one

    vol line (0,400) to (200,0)
    wt line (0,500) to (60,0)

    find intersection
    check profit at the orners

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