Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week. She noticed that when she reduces the price such that she earns $1 less in profit from each bouquet, she then sells three more bouquets per week. The relationship between her weekly profit, P(x), after x one-dollar decreases is shown in the graph below. Use the graph to complete each statement about this situation. The maximum profit the florist will earn from selling celebration bouquets is $___ . The florist will break-even after ______ one-dollar decreases. The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (___,____).

Answer 1

675

20

(0,20)

Explanation:

Answer 2

First space: 15

Second space: 20

Third space: 0

Fourth space: 20

Explanation:

If the florist decrease x times the value of the bouquet by 1, the number of bouquets sold is 30 plus 3 times x, so we have that:

P(x) = (20 - x)*(30+3x)

P(x) = 600 +30x - 3x2

The vertical axis of the graph represents the profit P(x) of the florist.

So observing the graph, we can see that the maximum profit is 675, and occurs when the value of x is 5, that is, the price of the bouquet is 20 - 5*1 = $15

Looking again to the graph, we see that when x = 20 her profit is zero (the price of each bouquet will be 20 - 20*1 = 0)

The interval of x for which the florist have a positive profit (P(x) > 0) is between x = -10 and x = 20, but the florist cannot make a negative number of one-dollar decrease, so the lower number in the interval should be 0.