batteries sizes

batteries sizes
What number of batteries per hour minimizes the cost?

A battery manufacturing plant spends C dollars per hour to produce “D”-size batteries. An efficiency consultant has determined that C is related to the number of batteries produced per hour, x, according to the equation C(x) = 0.01×2 – 2.6x + 245

in order to find the minimum you have to take the derivative of the equation above

C(x) = 0.01x^2 – 2.6x + 245

dc/dt=0.02x-2.6

now let that =0 so that you get a value for X

0=0.02x-2.6
0.02x=2.6
x=130

that would be the number of batteries that minimizes the cost


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