Math 22 Business and Economics Applications

Optimization in Business and Economics

1) Find the number of units $x$ that minimizes the average cost per unit ${\overline {C}}$ when $C=2x^{2}+348x+7200$

Solution:
Notice: ${\overline {C}}={\frac {C}{x}}={\frac {2x^{2}+348x+7200}{x}}=2x+348+{\frac {7200}{x}}$
Then, ${\overline {C}}'=2-{\frac {7200}{x^{2}}}=0$, so $x^{2}=3600$, so $x=\pm {\sqrt {3600}}=\pm 60=60$ since $x$ is positive.

Return to Topics Page

This page were made by Tri Phan