Question

the revwnue (in millions of dollars) from the sale of x units at a home supply outlet is given by R(x)=0.25x. the profit (in millions of dollars) from the sale of x units is given by P(x)=0.081x-0.7.

A. find rhe cost equation

B. find the cost of producing 7 units

C. what is the break even point

please show all work

Answer 1

Cost Function: Given, Revenue Function R(x)= 0.25% Profit Function P(x)= 0.081x -0.7 (A) We have to find the Cost function. Since Cost function is the difference of Revenue function and profit function, therefore C(x)= R(x)-P(x) =0.25x -0.081x +0.7 = 0.169x+0.7 Hence, the required cost equation is C(x)=0.169x+0.7 (B) We have to find the cost of producing 7 units.

Put x = 7 in the cost equation obtained in part (A), we get C(7)=0.169x7+0.7 =1.883 Hence, the cost of producing 7 units is 1.883 millions of dollars. (C) We have to find the break-even point. Break-even point is point where revenue is equal to the cost that is no profit. Therefore, P(x)=0 0.081x-0.7=0 0.7 x= 0.081 x9 Hence, the break-even point is achieved after selling 9 units.