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Anonymous asked in Science & MathematicsMathematics · 1 month ago

MATH HW HELP COLLEGE?

The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and 

1/2 hour to paint, and the economy model requires 2 hours to assemble and 1 hour to paint. The maximum number of assembly hours available is 24 per day, and the maximum number of painting hours available is 8 per day. If the profit on the deluxe model is $94 per unit and the profit on the economy model is $72 per unit, how many units of each model will maximize profit?

_______ deluxe units

_______ economy units 

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  • 1 month ago
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    Let d be the number of deluxe models; let e be the number of economy models.

    Maximize P = $94d + $72e

    subject to the following constraints:

    3d + 2e <= 24, This is the assembly constraint.

    0.5d + 1e <= 8. This is the painting constraint.

    d >=0

    e >= 0

    When you graph the constraints, you will find the "corners" where the constraints meet to form the "feasible region." By linear programming theory, the optimal solution must exist at one of these corners. In this problem, the ordered pairs (e, d) are (0,8), (6,4) and (8,0).

    Trying these out on the objective function for (0,8) gives P = 0(72) + 8(94) = $752.

    Trying these out on the objective function for (8,0) gives P = 8(72) + 0(94) = $576.

    Trying these out on the objective function for (6,4) gives P = 6(72) + 4(94) = $808.

    Therefore profit is maximized at $808 with 4 deluxe units and 6 economy units.

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