Question

The cost, C C, of producing x x Totally Cool Coolers is modeled by the equation C = 0.005 x 2 − 0.25 x + 12 C=0.005x2-0.25x+12 How many coolers need to be produced and sold in order to minimize the cost? (Round to the nearest whole number.)

Answer 1

Answer:

25 coolers are need to be produce and sell in order to minimize the cost.

Explanation:

$C = 0.005x^2-0.25x+12$ ..[1]

Differentiating the given expression with respect to dx.

$\frac{dC}{dx}=\frac{d(0.005x^2-0.25x+12)}{dx}$

$\frac{dC}{dx}=0.01x-0.25+0$

Putting ,$\frac{dC}{dx}=0$

$0=0.01x-0.25+0$

$0.01x=0.25$

x = 25

Taking second derivative of expression [1]

$\frac{d^2C}{dx^2}=\frac{d(0.01x-0.25)}{dx}=0.01$

$\frac{d^2C}{dx^2}>0$ (minima)

25 coolers are need to be produce and sell in order to minimize the cost.