Question

Question 1

1. A manufacturer of men’s shirts determines that her costs will be $500 for overhead plus $9 for each shirt made. Her accountant has estimated that her selling price p should be determined by p = 30 − 0.2 √ q, where q is the number of shirts sold. The quantity that should be produced in order to maximize profit is __________.

   	A.	q = 5685
   	B.	q = 4900
   	C.	q = 3650
   	D.	q = 1400

Answer 1

Ans.

b. q = 4900

Profit = Total revenue(TR) - Total cost (TC)

TR = price * quantity

TR = (30 - 0.2 ) q

TR = 30 q - 0.2 q ^{3 / 2}

TC = 500 + 9*number of shirts = 500 + 9 q

Profit = 30 q - 0.2 q ^{3 / 2} - (500 + 9 q)

Profit = 30 q - 0.2 q ^{3 / 2} - 500 - 9 q

Profit = 21 q - 0.2 q ^{3 / 2} - 500

Taking derivative with respect to q , we get

d profit / d q = 21 - 0.3 q ^{1 / 2}

21 - 0.3 q ^{1 / 2} = 0

21 = 0.3 q ^{1 / 2}

21 / 0.3 = q ^{1 / 2}

= 70

q = (70) ²

Thus q = 4900