Florist Florence buys flowers wholesale at 49 dollars a bouquet. If she sells them at 50 dollars a bouquet, she makes a 10 dollar profit for each sale but she can only sell 500 bouquets. For every 1 dollar she raises the price above $50, the number of bouquets she can sell will reduce by 10. To maximize her profit, what should be her selling price per bouquet?
I'm a bit confused with part of your question, "If she sells them at 50 dollars a bouquet, she makes a 10 dollar profit for each sale." Was 10 a mistypo of 1? I'm going to assume that it was a typo since I can't figure out what if would mean otherwise.
First, let's set x as the number of dollars she raises above $50.
That would mean that she sells each bouquet at 50 + x, meaning that her profit would be 50 + x - 49 = 1 + x.
It would also mean that the number of bouquets she's able to sell is 500 - 10x.
Then, the profit in total is (500 - 10x)(1 + x)
The goal is to find the value of x that creates the largest answer in this equation, (500 - 10x)(1 + x).
You could simply graph it out, or you can start simplifying.
(10)(50 - x)(1 + x)
We want to make it so that (50 - x) is as close to (1 + x) as possible.
50 - x = 1 + x
51 = 2x
25.5 = x
Since we're looking for her selling price (50 + x).
We just need to plug x in.
50 + 25.5 = 75.5
I hope this helped. :)))))