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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2=3600} , so Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=\pm\sqrt{3600}=\pm 60=60} since Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} is positive.

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