A software company estimates that the number of copies x , measured in thousands

Question

A software company estimates that the number of copies x, measured in thousands, of its new application that will sell when the price is p dollars per copy (up to $100) satisfies the equation

2px2 + 3px = 52,000.

Find

dx/dp

when the price is $40 per copy. (Round your answer to three decimal places.)
thousand

Interpret your result.

When the price increases from $40, the number of copies that will sell decreases at a rate of ______ thousand  ---Select--- dollars per copy increase copies per dollar increase .

Explanation / Answer

2px2+3px =52000

at p=40

80x2+120x -52000=0

x=24.756

2px2+3px=52000

4px dx + 2x2 dp + 3x dp + 3p dx=0

dx(4px +3p) + dp(2x2+3x)=0

dx/dp= -(2x2+3x)/(4px+3p)

at p=40 and x=24.756

dx/dp= -0.105

So the number of copies sell decrease at the rate of -0.105 thousand

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