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notsponge [240]
3 years ago
7

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 H

ow many coolers need to be produced and sold in order to minimize the cost? (Round to the nearest whole number.)
Chemistry
1 answer:
neonofarm [45]3 years ago
3 0

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.

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