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The weekly profit P for a widget producer is a function of the number n of widgets sold. The formula is as follows, where P is measured in thousands of dollars, n is measured in thousands of widgets, and the formula is valid up to a level of 10 thousand widgets sold.

P = −4 + 2.5n − 0.2n2

 

At what sales level is the profit as large as possible? (Use the graph to find the value. Round your answer to the nearest whole number.) ?

 

 

n= _______ thousands of widgets 

 Oct 13, 2015
 #1
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P = −4 + 2.5n − 0.2n^2

 

Profit greatest when dP/dn=0

 

dP/dn = 2.5-0.4n

2.5-0.4n=0

2.5=0.4n

2.5/0.4=n

n=6.25 thousand widgets

n=6 thousand widgets to the nearest 1000.

 

 

Here is the graph to back up my answer.  

https://www.desmos.com/calculator/ula6msgsc8

 Oct 13, 2015

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