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Phil makes and sells rugs at his roadside stand. His monthly fixed cost for owning the stand is $1075. If he makes and sells 19 rugs, his total costs are $1227 and he brings in $627 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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Jseberrio

Answer:

Monthly cost (Total cost):

[tex]Total cost (TC)=1075 + 8X[/tex]

Monthly revenue (Total revenue):

[tex]Total revenue(TR)=33X[/tex]

Monthly profit (Total profit):

[tex]Total profit (TP) = 25X - 1075[/tex]

Explanation:

Ok, firts we organice our information:

Fixed cost (FC) = 1075

Rugs produced (X) = 19

Total cost if the production is 19 rugs = 1227

Total Revenue if the production is 19 rugs = 627

We can find the Total cost function from the information provided:

[tex]Total cost=Fixed cost(FC) + Variable cost(VC)[/tex]

[tex]1227=1075 + VC(X)[/tex]

[tex]1227=1075 + VC(19)[/tex]

[tex]VC(19)=1227- 1075[/tex]

[tex]VC=\frac{152}{19}[/tex]

[tex]VC=8[/tex]

We now replace in the Total cost function:

[tex]Total cost  (TC)=1075 + 8X[/tex]

We con now find the total revenue:

[tex]Total revenue (TR) = Price(P)*Quantity(X)[/tex]

[tex]627=P*19[/tex]

[tex]P=\frac{627}{19}[/tex]

[tex]P=33[/tex]

Now we replace in the Total revenue function:

[tex]Total revenue(TR)=33X[/tex]

Having the TC and TR function we find the Profit function:

[tex]Total profit (TP) = TR - TC[/tex]

[tex]Total profit (TP) = 33X - (1075 + 8X)[/tex]

[tex]Total profit (TP) = 33X - 1075 - 8X)[/tex]

[tex]Total profit (TP) = 25X - 1075[/tex]

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