Question

A television manufacturer produces x sets per week so that the total cost of production is given by the relation TC=q^3-195q^2+6600q+15,000. Find how many television set must be manufactured per week to minimize total cost.

Answer 1

$TC=q^3-195q^2+6600q+15,000$

Differentiating w.r.t. q:

$=3q^2-390q+6600$

Equating above equation to zero:

$3q^2-390q+6600=0$

Solving the quadratic equation using quadratic formula:

$Q=145.$