SOLUTION: If the function C=2x^2-52x+338 can be used to predict the cost of manufactoring x shirts per hour for Company Z, How many shirts should Company Z make per hour if they want to mini

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Question 378070: If the function C=2x^2-52x+338 can be used to predict the cost of manufactoring x shirts per hour for Company Z, How many shirts should Company Z make per hour if they want to minimize the hourly cost of production?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
This problem can be solved using precalculus methods, but the general method to solve such a problem requires calculus. I'll present both solutions:
Since C is a 2nd degree polynomial, the vertex of the polynomial occurs at x+=+-b%2F2a+=+52%2F4+=+13+%28shirts%29. The polynomial points upward, therefore 13 is the minimum.
Or, we may take the derivative of C using the Power Rule: dC%2Fdx+=+4x+-+52. The derivative equals zero when x = 13, and it can be checked that 13 is the minimum.