Question

ur college newspapes, The Collegiate Investigator, sells for 90 per copy. The cost of producing x copies of an edition is given by C(x) 60+0.10x+0.001x2 dollars. (a) Calculate the marginal revenue R(x) and profit P(x) functions. HINT [See Example 2.) P(x) (b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition. profit marginal revenue marginal profit per additional copy per additional copy Interpret the results. The approximate ! loss v] from the sale of the 501st copy is 40 (c) For which value of x is the marginal profit zero? x400 copies Interpret your answer The graph of the profit function is a parabola with a vertex at x so the profit is at a maximum when you produce and sell eed Help? Emani

Answer 1

a) TR = 0.9X
MR = 0.9
Profit = TR-TC = 0.9X-(60+0.1X+0.001X^2) = 0.9X-60-0.1X-0.001X^2= 0.8X-60-0.001X^2

b) Revenue = 0.9*500 =$450
Profit = 0.8*500-60-0.001*500^2 = 90
MR = 0.9 per additional copy
Marginal profit = 0.8-(0.0001*2*500) = 0.7
The approximate loss from the sale of 501st copy is 0.2
Profit from 500 =0.8*500-60-0.001*500^2 = 90.00
Profit from 501 =0.8*501-60-0.001*501^2 = 89.8

c) X=400

d) Vertex at X= 83, so the profit is at a maximum when you produce and sell 400