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10 August, 22:25

Phil makes and sells rugs at his roadside stand. His monthly fixed cost for owning the stand is $800. If he makes and sells 19 rugs, his total costs are $952 and he brings in $456 in revenue. Find Phil's monthly cost, revenue, and profit functions (assuming they are linear). Let x be the number of rugs made and sold each month.

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  1. 10 August, 22:29
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    Total Cost is given as:

    Total cost = Fixed cost + Variable cost

    Fixed cost = $800

    Total cost = $952

    Total Variable cost = Total cost - Fixed cost

    = 952 - 800

    = 152

    Therefore, Variable cost per rug is

    = 152 : 19

    = $8 per rug

    Therefore we can write the cost function as;

    C (x) = 800 + 8x

    Revenue for 19 rugs = $456

    Revenue per rug = 456 : 19

    = 24

    Therefore, total revenue;

    R (x) = 24x

    Now, we can evaluate profit using the following formula;

    Profit = Revenue - Cost

    P (x) = 24x - (800 + 8x) = 24x - 800 - 8x

    P (x) = 16x - 800
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