SOLUTION: A fast food restaurant sells 200 Megaburger combos daily at $4.59 each. Every 10 cents procee increase reduces sales by 3 combo meals. Find the maximum income from Megaburger combo

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Question 1120631: A fast food restaurant sells 200 Megaburger combos daily at $4.59 each. Every 10 cents procee increase reduces sales by 3 combo meals. Find the maximum income from Megaburger combo sales and the price for which they should be sold.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let's work the problem in cents instead of dollars to avoid having to work with the decimals....

The current price is 459; at that price they sell 200 a day. The total revenue is 200(459) = 91800, or $918.

For each price increase of 10 cents, the number sold per day will decrease by 3. So if the price increases by 10 cents x times, the price will be (459+10x) and the number sold will be (200-3x).

The total revenue will then be

%28459%2B10x%29%28200-3x%29+=+-30x%5E2%2B623x%2B91800

The maximum value of a quadratic function ax^2+bx+c is when x = -b/2a. For this problem, x = -623/-60 = 10.38. Since x has to be a whole number, the maximum revenue will be when x=10.

So the maximum revenue will be when the price is 459+10(10) = 559, or $5.59. The revenue will be -30(10^2)+623(10)+91800 = 95030, or $950.30.