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

Question

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

Answer 1

-.2x^2 + 90x -260

P'(x) = dP/dx = MP = Marginal Profit = -.4x +90

P'(40) = -.4(40) +90 = -16 + 90 = $74 per unit

Average Profit = AP = P/x = -.2x + 90 -260/x

P(40)/40 = -.2(40) + 90 -260/40 = -8 +90 - 13/2 = 90-14 1/2 = 75 1/2 = $75.50 average profit

"Marginal Average Profit"?? That's a new one, MAP? does not compute

although in this case 74 is very close to 75.5, virtually the same: marginal = average, almost

profit maximizing output level is where MR = MC and MC =AC when AC is at a minimum