Phil makes and sells rugs at his roadside stand. His monthly fixed cost for owning the stand is $527. If he makes and sells 22 rugs, his total costs are $703 and he brings in $550 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.
Phil makes and sells rugs at his roadside stand. His monthly fixed cost for owning the stand is $527. If he makes and sells 22 rugs, his total costs are $703 and he brings in $550 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.
C(x) =
R(x) =
P(x) =
Cost for owing the stand = $527. This is fixed cost.
Total cost = $ 703.
Number of rugs sold = 22.
Revenue from 22 rugs = $ 550.
Cost of rugs = total cost - fixed cost = $ 703-$527 = $ 176
Cost of each rug = 176/22 = $8/rug.
So, the cost function can be written as,
C(x) = 527+8x, where x is the number of rugs.
Again, revenue from each rug = 550/22 = $ 25/rug
So, the revenue function R(x) = 25x
Profit is calculated by subtracting the cost function from revenue function,
So, P(x) = 25x - ( 527+8x)
=17x-527
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