Convert The Function

Algebra Level 3

XYZ, inc. produces widgets at a cost of $12 a widget. After analyzing the demand for their widgets at various price levels, they have come up with the following function to model the demand at each price level:

D ( x ) = − 200 x + 7000 D(x) = -200x+7000

How can XYZ, Inc. convert the function D ( x ) D(x) into the function R ( x ) R(x) that will model the revenue generated at each price level?

Multiply D(x) by x. Multiply D(x) by 12. Not Enough Information

Justin Malme by Justin Malme , 36, USA

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1 solution

Justin Malme
Jun 9, 2016

Revenue is calculated by taking the price of the unit multiplied by the number of units sold. If inputting a price x x in D ( x ) D(x) will get us how many units will sell at that price, then we need to multiply D ( x ) D(x) by x x to model the revenue generated at each price x x . Multiplying D ( x ) D(x) by the cost of $12 would actually create a function to model the total cost of the units sold a price x x .

The revenue function would then be R ( x ) = − 200 x 2 + 7000 x R(x) = -200x^2+7000x

For Example:
at x = $ 10 x=\$10 , D ( 10 ) = 5 , 000 D(10) = 5,000 units, and $ 10 × 5 , 000 = $ 50 , 000 \$10 \times 5,000 = \$50,000 in revenue.
R ( 10 ) = − 200 ( 10 ) 2 + 7000 ( 10 ) = − 20 , 000 + 70 , 000 = $ 50 , 000 R(10) = -200(10)^2+7000(10) = -20,000+70,000 = \$50,000 in revenue.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Hi Justin

Nice problem! I would like to recommend you to add more options, perhaps, because solving this problem using elimination becomes really easy.

That's all, Thanks! Also, good solution :)

Mehul Arora - 5 years ago

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A bit on Tidying up your LaTeX: The code for × \times is ( \times \ )

Mehul Arora - 5 years ago

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Thanks for catching that! I didn't even notice I did that.

Justin Malme - 5 years ago

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@Justin Malme – That's awesome! Neat solution.

And about adding more options, I think adding more options is always beneficial, regardless of the number of solvers.

Just a thought though, keep that in mind for future problems

Good luck!

Mehul Arora - 5 years ago

I thought about adding some more options; but as of now the problem only has a 27% solve rate, so I decided to leave it as-is. Thanks for the input!

Justin Malme - 5 years ago

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