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.

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