Phil makes and sells rugs at his roadside stand. His monthly fixed cost for owning the stand is $987. If he makes and sells 18 rugs, his total costs are $1131 and he brings in $522 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.

Question
Asked Sep 5, 2019
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Phil makes and sells rugs at his roadside stand. His monthly fixed cost for owning the stand is $987. If he makes and sells 18 rugs, his total costs are $1131 and he brings in $522 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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Expert Answer

Step 1

If phil sell 18 rugs and bring in $522 revenue.

So selling price of a rug = $522/18 = $29.

So revenue function  R(x) = 29x                 ...(1)

 

Step 2

Phil cost for making 18 rugs = $1131 - $987 = $144

So his variable cost = $144/18 = $8 per rug

So cost function is C(x) = 987 + 8x           ...

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