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# Help

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Florist Florence buys flowers wholesale at \$40 a bouquet. If she sells them at \$50 a bouquet, she makes a \$10 profit for each sale but she can only sell 500 bouquets. For every \$1 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?

Sep 18, 2022

#1
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Florist Florence buys flowers wholesale at \$40 a bouquet. If she sells them at \$50 a bouquet, she makes a \$10 profit for each sale but she can only sell 500 bouquets. For every \$1 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?

Her purchase price is the same irrespective of the selling price,

so let's just see what will maximize the total selling price.

Price   Number Sold   Income

50           500            25,000

51           490            24,990

52           480            24,960

53           470            24,910

I think I'm seeing a trend here.  A couple more...

60           400            24,000

70           300            21,000

I've seen enough.  Have you?  She comes out best selling 500 for \$50 each.

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Sep 18, 2022
#2
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Wait a minute.  Too late to edit my above.  Does the problem mean she has to buy only as many as she sells?  In that case.

Price   Number Sold   Income      Cost       Profit

50           500            25,000     20,000    5,000

51           490            24,990     19,600    5,390

52           480            24,960     19,200    5,760

53           470            24,910     18,800    6,110

This isn't shaping up like I thought it would.

We've got to find where it breaks over.

60           400            24,000     16,000    8,000

69           310            21,390     12,400    8,990

70           300            21,000     12,000    9,000

71           290            20,590     11,600    8,990

It looks like the profit maxes out at 300 bouquets at \$70 each

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Sep 18, 2022