HI Mike…Thanks for all your help ! Here’s another question:

When a buffet restaurant charges $12.00 per meal, the number of meals it sells per day is 400. For each $0.50 increase to the price per meal, the number of meals sold per day decreases by 10. What is the price per meal that results in the greatest sales, in dollars, from meals each day?

A) $16.00
B) $20.00
C) $24.00
D) $28.00

Fun! Let’s write a function for the total dollar value of sales. First, in words: [dollars in sales] = [meals sold] × [price per meal].

Easy enough, right? Now, can we write expressions for [meals sold] and [price per meal] using the same variable? I think we can.

Let’s say x equals the number of $0.50 price increases applied.

Each time a price increase is applied, the restaurant loses 10 sales, so we can say [meals sold]=400-10x. Right? 

Each time a price increase is applied, the restaurant gets more money per meal. So we can say [price per meal]=12.00+0.50x. Now put it all together:

[dollars in sales] =(400-10x)(12+0.5x)

Now, graph that and see where the sales peak is. (I’d put an image here of my own calculator but its batteries are dead. Womp womp.)

You’ll hopefully see that after 8 price increases, the restaurant’s sales are $5,120, and that’s as high as they get.

The question asked for the price, not the number of increases, so we have just one more step. What’s the price after 8 increases? Well, [price per meal]=12+0.5(8) = 16. Choice A is the answer. 



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