Problem 2 Easy Difficulty

A company estimates that the marginal revenue (in dollars per unit) realized by selling $ x $ units of a product is $ 48 - 0.0012x $. Assuming the estimate is accurate, find the increase in revenue if sales increase from 5000 units to 10,000 units.

Answer

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Video Transcript

Okay, So our question gives us a marginal revenue function of 48 minus 0.12 x and asked if sales jumped from 5000 to 10,000. What with the increase in revenue Be so for all of these economics formula. Whenever you hear the word marginal, think derivative. So in this case, this marginal revenue function I'm going to indicate as or prime of X and then if we want the increase from 5000 to 10,000 we really want for quantity air of 10,000 minus air. 0 5000 And so on the side I've written the net, changed the room with the f of a term moved. This might be how you see it, depending on what source you look at. And here is a pretty straightforward application. If we want our of 10,000 minus or a 5000 and we have our prime of X, we just need to integrate from 5000 to 10,000. So finishing the formula set up for the serum you have the integral from 5000 to 10,000 of 48 minus 0.12 x dx, which is going to be 48 x from 5000 to 10,000 minus 0.0 I want to over too X squared from 5000 to 10,000 plugging in. We get 48 times 10,000 minus 5000 is 5000 minus this coefficient which becomes 0.0 06 and then 10,000 squared would be 100 million, 5000 squared would be 25 million so we're left with 75 million, which is 240,000 minus 45,000 or the final answer of $195,000.