Question

Antonio and Bendu want to earn money this summer by setting up a lemonade stand. Thinking about last summer's sales, they realize that they sold an average of 200 cups per day when they charged $1.00 per cup. Other vendors with similar sales have noted that for every $.25 increase in price, they sold 20 fewer cups. Using this information, what should they charge to maximize their income? And what is the function and plot points of this problem?

GUYS PLEASE HELP ME OUT ON THIS IM DESPERATE AND USED 50 POINTS FOR THIS. AND DON'T TRY AND COPY AND PASTE THE QUESTION, BELIEVE ME, I'VE TRIED.

Answer 1

1.) From the information given, they should charge $1.25 per cup to maximize their income

2.) Function y = -1.25x + 200

3.) (200, 200) and (180, 225)

Explanation:

Let assume that they sold an average of 200 cups per day when they charged $1.00 per cup. Then they will realise $1.00 × 200 = $200 per day

If they increase the price by $ 0.25, they sold 20 fewer cups. That is, they will realise $1.25 × 180 = $225

Increase in profit = 225 - 200 = $25

From the information given above, they should charge $1.25 per cup to maximize their income

If income = y and number of cup = x

Slope = 25/-20 = - 1.25

Function y = -1.25x + 200

The plot point are:

(200, 200) and (180, 225)