# 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.)

1 answer

###### 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.)

## Answers

Answer:25 coolers are need to be produce and sell in order to minimize the cost.Explanation:[tex]C = 0.005x^2-0.25x+12[/tex] ..[1]Differentiating the given expression with respect to dx.[tex]\frac{dC}{dx}=\frac{d(0.005x^2-0.25x+12)}{dx}[/tex][tex]\frac{dC}{dx}=0.01x-0.25+0[/tex]Putting ,[tex]\frac{dC}{dx}=0[/tex][tex]0=0.01x-0.25+0[/tex][tex]0.01x=0.25[/tex]x = 25Taking second derivative of expression [1][tex]\frac{d^2C}{dx^2}=\frac{d(0.01x-0.25)}{dx}=0.01[/tex][tex]\frac{d^2C}{dx^2}>0[/tex] (minima)25 coolers are need to be produce and sell in order to minimize the cost.

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