A manufacturer of mens shirts determine that its costs will

A manufacturer of men\'s shirts determine that its costs will be 500 dollars for overhead plus 9 dollars for each shirt made. A market analyst has estimated that the price p, in dollars, at which the shirts are offered to the customers is related to the number x of shirts bought are related by the equation y + 0.2 squareroot x - 30 the manufacturer always prices the shirts at the highest price at which all of them will be sold. How many shirts have to be made and sold in order to obtain the maximum possible profit? 22500 4900 11025 8100 None of the above answers is correct

Solution

manufacturing cost of x no. of shirts: c = 500 +9x

selling price : p = 30 - 0.2sqrt(x)

Profit : P(x) = p - c = 30 - 0.2sqrt(x) - (500 +9x)

= - 470 -9x - 0.2sqrx

To find maximum profit Find :P\'(x) = -0.1/sqrt(x) -9

P\'(x) =0 ; x=0

None of above