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?
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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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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