Question

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.

A graph for p of x is a downward open parabola with its vertex at (5, 725) and passes through the points (negative 10, 0), and (20, 0).

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

We use the attached graph

a. The maximum profit is the y value that is the value of P(x) that reaches maximum. From the graph the maximum value of P(x) is 675

So the maximum profit the florist will earn from selling bouquets = $675

b. Break even is the point where the profit p(x) becomes 0

From the graph we can see that P(x) =0 at x= -10 and x=20

x=-10 is invalid

So, break even after 20 one- dollar decreases

c. The interval of number of one dollar decreases is where the profit P(x) is greater than 0.

From the graph its very clear that the profit P(x) is greater than 0 in the interval 0 to 20.

So, The interval of number of one dollar decreases for which the florist makes a profit from celebration bouquet is (0, 20)