Answer to Question #274900 in Calculus for nnn

Question

1.   You wanted to start your business of manufacturing custom made mobile covers for the newest model of iPhone. The selling price is  per cover. The cost function to manufacture the covers is  where  is the number of covers sold. Show at least 5 decimal places

a.   Find the profit function . 3 Marks

b.     Find the quantity  that maximizes profit. 2 Marks

c.     Explain the steps you take to arrive at your answer in part b. 3 Marks

d.     Interpret the answer. 2 Marks

Answer 1

a.

profit function:

$P(x)=R(x)-C(x)$

where R(x) is revenue function,

C(x) is cost of producing function

$R(x)=xp(x)$

where p(x) is selling price function,

x is number of units sold

b,c,d

to find the quantity  that maximizes profit:

we have to find extremums of P(x) from condition:

$P'(x)=0$

P(x) has local minimum or maximum at the roots of given equation

if P'(x) change sign from "+" to "-" then point of extremum is maximum, so

this value of x maximizes profit