a florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30…

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 the 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 ( , ).

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 the 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

Explanation:

Step1: Identify maximum profit

The maximum point on the graph of $P(x)$ gives the maximum profit. Looking at the graph, the $y -$ value of the vertex is the maximum profit. The highest point on the graph has a $y -$ value of $675$.

Step2: Find break - even points

The florist breaks even when $P(x)=0$. The graph intersects the $x -$ axis at $x=- 10$ and $x = 20$. The number of one - dollar decreases for break - even is the non - negative value of $x$ where $P(x) = 0$. So the florist breaks even after $20$ one - dollar decreases.

Step3: Determine profit interval

The florist makes a profit when $P(x)>0$. This occurs when the graph is above the $x -$ axis. The $x$ values for which the graph is above the $x -$ axis are in the open interval $(-10,20)$.

Answer:

The maximum profit the florist will earn from selling celebration bouquets is $$675$. The florist will break - even after $20$ one - dollar decreases. The interval of the number of one - dollar decreases for which the florist makes a profit from celebration bouquets is $(-10,20)$.