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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.)

User Niksac
by
8.7k points

1 Answer

2 votes

Answer:

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.

User Aethyn
by
8.2k points
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