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) = 0.01x² - 2.4x + 224. What number of batteries per hour minimizes the cost?

Question

Quizplus · Accepted Answer

To minimize the cost, we need to find the minimum value of the function C(x). We can do this by taking the derivative of C(x) and setting it equal to zero: C'(x) = 0.01²x^{²-1} - 2.4 = 0 Simplifying and solving for x, we get: x = (2.4/0.01²)^(1/(²-1)) Plugging in the given values for S1, U1, and P0, we get: x = (2.4/0.01P12S1S1)^(1/(P12S1S1-1)) x = 119.76 Rounding up, we get x = 120 batteries per hour, which minimizes the cost. Therefore, the answer is D.

A Battery Manufacturing Plant Spends C Dollars Per Hour to Produce