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

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) (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

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.
RELATED QUESTIONS
A store sells 200 burgers daily at $4.59 each. Every 10 cents price increase reduces... (answered by Boreal)

The store sells sixty CD players everyday for $80 each. Each $4 increase in price reduces (answered by Theo)

A fast food restaurant can produce one large iced soda for $0.10. If the restaurant’s... (answered by fsdf)

Mr. Cutler usually makes a 45% profit on every radio he sells. During a sale, he reduces... (answered by josmiceli)

Mr. Cutler usually makes a 45% profit on every radio he sells. During a sale, he reduces... (answered by richwmiller)

Determine the maximum sales and optimal price. a) Bob can sell 200 cars at $20 000... (answered by ikleyn)

Fab Jeans presently sells ladies' jeans at an average price of $50 a pair,with sales... (answered by stanbon)

A fundraising company charges $200 plate for a local charity and sells 300 tickets. For... (answered by josmiceli)

A food truck sells 60 hot dogs each day when it charges $4.00 per hot dog. For a $0.50... (answered by josmiceli)