Expert: Scott A Wilson - 12/8/2009

Question
This is a bonus question from last week's alegebra assignment. I didn't answer correctly, and I'd like to know how to be able to figure it out :) Please help -Thank you!!

Isis sells lemon ices at her lemonade stand. She charges $1.20 per ice and sells an average of 50 per day. If she could sell one more ice each day for each 2 cents she decreased the price, at what price should Isis sell her ices to maximize her income from them?

Answer
She sells 50, and it would go up by n.
She charges 1.20, and that would go down by 0.02n.

The equation is f(n) = (50+n)(1.20-0.02n).
That is f(n) = 60 + 0.2n - 0.02n².
The derivative is f'(n) = 0.2 - 0.04n.

Set this to 0, alter it, and get 0.2 = 0.04n.
Divide both sides by 0.04 to get the answer.

Now 0.2/0.04 = 5, so n = 5 is how many more blocks she would sell for a 10c decrease in price.