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

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

Step-by-step explanation:

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

Differentiating the given expression with respect to dx.

`(dC)/(dx)=(d(0.005x^2-0.25x+12))/(dx)`

`(dC)/(dx)=0.01x-0.25+0`

Putting ,
`(dC)/(dx)=0`

`0=0.01x-0.25+0`

`0.01x=0.25`

x = 25

Taking second derivative of expression [1]

`(d^2C)/(dx^2)=(d(0.01x-0.25))/(dx)=0.01`

`(d^2C)/(dx^2)>0` (minima)

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