Question

60 3) Suppose that the cost of manufacturing x bicycles is given by C(x) = 10 + 5x + **3. The company determined that the demand function for the bicycle is given by p 90 - x where p represents the price in dollars. [3+4= 7 marks] = a) Find and interpret C'(10). b) Find the maximum weekly profit. [Be sure to verify that the profit is maximum]

Answer 1

<sup>ca) AM The cost of manufacturing a bicycles is given by Clu) = 10+ 5x + 1 x The company determined that the demand function for the bicycle is given by P = gon, where p represents the price in dollars. c'(x) = d (10+54 + 1 x) = 0+ 5 + 1/ 138²) = 5 + 1 1 ² .. ('(10) = 5+10 (1082 =5+100) = 5+5=10 c'<10)=10 "The marginal cost at the production level of lo units, the additional cost is $10, it one more unit be produced. (b) Given, demand function p=goox Revenue function, R(W) = Pse = 90-W)x=90x-x "Profit P (n) = R(1)C(x) = (90x-w²)-(10+5x+tox?) gou-n-10-50-tox? Plu) = -1 3 x 3 = x+854-10 differentiating with respect to t P'(n) = -1 4 ² - 2x .2k+85 for max./min. of P(x) P'lu) 20 --x-2x+85-0 x² +401 - 1700=0 >=-40+1 40² 4 11 (-1700) -40 I J 8400 -40+ 2051 2(1) 2 = -65:825757, 25.825757 but a cannot be negative in=25.825757 Now. P"(nl=- 1 2 - 2 2

.:P"(25.825751)=(25.825757)-2 E-4.5825757 CO . Prosit is maxinium, when n=25.825757 maximum profit=P (25.825757) (25.82575 5757)= (25.825757)? +85(25.825157)-10 GO - 1231-14 maximum profit = $1231.14</sup>