Answer to Question #104082 in Calculus for mm

Question

The cost of production of a substance per unit is given by the formula C = q^2 - 4q +1 , where q is the material cost. Find the selling price per unit, so that the profit on 100 units will be Rs.200, if q = 15 . Also calculate the cost of material per unit so that profit of 100 units can be maximized,
if the selling price is Rs. 200.

Answer 1

1) TP = p×Q - C = 100p - 15^2 + 4×15 - 1 = 200,

100p = 366,

p = 3.66.

2) TP is maximized, when TP' = 0,

TP' = -C'(q) = 0,

2q = 4,

q = 2.