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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?

 Jan 1, 2021
 #3
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PLeasssse hellpppp! I really need it. Thanks in advance

 Jan 1, 2021
 #4
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CPhill plssssss helpp

 Jan 1, 2021
 #5
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Hello Guest!

 

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. 

 

Variables

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)

 

Equation

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

 

Answer

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. :)))))

=^._.^=

 Jan 1, 2021
 #6
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Wait im sorry it was supposed to be 40 not 49!! Sorry about that mistake!

Guest Jan 1, 2021
 #7
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Oh, dw about it. 

Do you understand the logic behind the explanation?

 

=^._.^=

catmg  Jan 1, 2021
 #8
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Yep I do!! Thank you so much!

Guest Jan 1, 2021
 #9
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Nice job catmg!!

wolfiechan  Jan 2, 2021

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