Question

A bakery sells, on average, 100 special breads per day and collects with these sales, on average, R $ 300.00. It was found that the quantity of special breads sold daily increases if the price is reduced, according to the equation q = 400 - 100p, in which q represents the quantity of special breads sold daily and p, its price in reais. In order to increase the flow of customers, the bakery manager decided to run a promotion. To do so, it will modify the price of special bread so that the quantity to be sold daily is as large as possible, without decreasing the average daily collection on the sale of this product. The price p, in reais, of the special bread in this promotion should be in the range
a) R $ 0.50 p b) R $ 1.50 p c) R $ 2.50 p d) R $ 3.50 p e) R $ 4.50 p

Answer 1

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Answer 2

If the price is p and the quantity of bread sold is q = 400 - 100p, the average collection, in reais, depending on the price p, is given by R (p) = (400 - 100p). P

For this collection to be R $ 300.00, you must have:

(400 - 100p). p = 300 ⇔ 4p - p² = 3 ⇔ p² - 4p + 3 = 0 ⇔ p = 1 or p = 3

R $ 300.00

The current price is R $ 3.00, as R $ 300,000 / 100 = R $ 3

To maintain the collection, the price must be lowered to R $ 1.00 (R $ 0.50 <R $ 1.00 <R $ 1.50)

ANSWER: letter A