The total profit (in dollars) from the sale of x charcoal grills is P(x)=90x−0.2x^2−260

Question

A) Find the average profit per grill if 40 grills are produced. 

Ave. profit = ?

Find the marginal average profit at a production level of 40 grills. 

(B) Marginal average profit =  ?

Use the results from parts (A) and (B) to estimate the average profit per grill if 41 grills are produced. 

(C) Estimated average profit = ?

Answer 1

(A) P_av(40) = P(40)/40 = (3600 - 320 - 260)/40 = 3020/40 = $75.50 per unit

(B) P_av = P(x)/x = 90 - 0.2x - 260/x; Marginal average profit P'av = - 0.2 + 260/x²_; P'_av(40) = -0.2 + 260/1600 =

-$0.0375 per unit

(C) P_av(41) ≈ P_av(40) + P_av'(40) = $75 - 0.0375 = $74.96 per unit