Suppose the total cost of producing x units of a particular

Suppose the total cost of producing x units of a particular commodity is C(x) = 2/5x^2+10x and the selling price is p(x) = 1/5(100- x) Determine the level of production that maximizes the profit.

Solution

Total Cost = (2/5)x^2 +10x

Total selling price =x/5(100 -x)

Profit ,P(x) = selling price - cost price

= -x^2/5 +20x - (2/5)x^2 - 10x

= -3x^2/5 +10x

Maximum Profit would occur at vertex of the quadratic function

x = -b/2a = -(10)/2*(-3/5)

= -10*5/-6

= 50/6

= 8 units (approximately)