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 Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle C=2x^{2}+348x+7200}

Solution:
Notice: Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\overline {C}}={\frac {C}{x}}={\frac {2x^{2}+348x+7200}{x}}=2x+348+{\frac {7200}{x}}}
Then, Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\overline {C}}'=2-{\frac {7200}{x^{2}}}=0} , so Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x^{2}=3600} , so $x=\pm {\sqrt {3600}}=\pm 60=60$ since $x$ is positive.

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