Difference between revisions of "Math 22 Business and Economics Applications"

Revision as of 06:24, 2 August 2020

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.

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 ==Optimization in Business and Economics==
+'''1)''' Find the number of units <math>x</math> that minimizes the average cost per unit <math>\overline{C}</math> when <math>C=2x^2+348x+7200</math>
+{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
+!Solution: &nbsp;
+|-
+|Notice: <math>\overline{C}=\frac{C}{x}=\frac{2x^2+348x+7200}{x}=2x+348+\frac{7200}{x}</math>
+|-
+|Then, <math>\overline{C} '=2-\frac{7200}{x^2}=0</math>, so <math>x^2=3600</math>, so <math>x=\pm\sqrt{3600}=\pm 60=60</math> since <math>x</math> is positive.
+|}
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 '''This page were made by [[Contributors|Tri Phan]]'''