Ron has 20 roses, 30 irises, 40 sunflowers, and 50 tulips. He wants to make as many bouquets as possible, with each bouquet containing at least 3 different kinds of flowers. A bouquet can be of any size. How many bouquets can he make?
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Ron has four types of flowers: 20 roses, 30 irises, 40 sunflowers, and 50 tulips. He wants to make as many bouquets as possible, with each bouquet containing at least 3 different kinds of flowers. Let's visualize this problem and find the optimal solution.
To solve this problem, we need to analyze the constraints. Each bouquet must contain at least 3 different flower types. With 4 flower types available, we have 4 possible 3-type combinations and 1 four-type combination. Using 3-type combinations will maximize the number of bouquets we can make.
The optimal solution uses a system of equations. Let x1 be R-I-T bouquets, x2 be R-S-T bouquets, and x3 be I-S-T bouquets. Solving the constraints gives us x1 equals 5, x2 equals 15, and x3 equals 25, for a total of 45 bouquets. This uses all roses, irises, and sunflowers, with only 5 tulips remaining unused.
Let's verify our solution visually. We have 5 bouquets of roses-irises-tulips, 15 bouquets of roses-sunflowers-tulips, and 25 bouquets of irises-sunflowers-tulips. This gives us exactly 45 bouquets total, using all available roses, irises, and sunflowers, with only 5 tulips remaining unused.
In conclusion, Ron can make a maximum of 45 bouquets. This solution uses all available roses, irises, and sunflowers, with only 5 tulips remaining unused. The efficiency is 95 percent, and this represents the optimal solution given the constraint that each bouquet must contain at least 3 different flower types.