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.

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)

Answer 2

Answer:

A candlemaker prices one set of scented candles at $10 and sells an average of 200 sets each week. He finds that when he reduces the price by $1, he then sells 50 more candle sets each week. A function can be used to model the relationship between the candlemaker's weekly revenue, R(x), after x one-dollar decreases in price.

Step-by-step explanation: