A tape manufacturer has a monthly fixed cost of 2000 It cost

A tape manufacturer has a monthly fixed cost of $2,000 It costs the manufacturer $0.25 to produce each box of tape. The price that they sell each box of tape at is determined by the price-demand function p(x) = -0.00125z + 705. Assuming that the cost functions is linear. Find the cost function. Find the revenue function. Find the profit function. How many boxes of tape must be made for the company to maximize their profit What is the selling pnee at this point

Solution

(a) fixed cost=82,000$

      variable cost=0.25x$ where x is the no of tape boxes produced

so cost function=fixed cost+variable cost

           C(x)=82,000+.25x

b)Revenue function R(x)= the no of tape boxes produced x price demand function p

                                   = x(-.00125x+7.5)

                                   =-.00125x²+7.5x

c) profit function S(x)= Revenue function R(x)-cost functionC(x)

                             =-.00125x²+7.5x-82,000-.25x

                            =-.00125x² +7.25x-82,000

d)Profit is maximized at the quantity of output where marginal revenue equals marginal cost

marginal revenue(MR)= dR(x)/dx   ;marginal cost (MC) =dC(x)/dx

               MR          =-.00250x+7.5    ;MC=.25

Now putting MR=MC

-.00250x+7.5=.25

x=7.25/.0025

x=2900 this is profit maximizing quantity

and price per unit is =-.00125x2900+7.5

                             =3.875$/unit

selling price=3.875x2900

                   =11237.5 $