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Problem 11 Easy Difficulty

A company modeled the demand curve for its product (in dollars) by the equation
$$ p = \frac{800,000e^{\frac{-x}{5000}}}{x + 20,000} $$
Use a graph to estimate the sales level when the selling price is $16. Then find (approximately) the consumer surplus for this sales level.

Answer

consumer surplus $\approx \$ 37,753$

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Video Transcript

Okay, so here we have the demand curve, and here we have globally line right here. We have the price of $16 so we just seem to see where they're going to intersect, which is about 3727. So now what I need to do is integrate dysfunction. The demand function from zero 2 3727 No B e negative X over 5000 over X plus 20,000 d X. So you'll you'll. You'll want to use a computer at algebra system for this one, such as Wolfram, and then whenever you do, you will get about $37,753.

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