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# Setting up constraints for profit maximization

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A florist is planning to make up floral arrangements for the upcoming holiday weekend. He has following supply of flowers in stock this Friday and he cannot get any more.

Type------Number available------Cost per flower

Roses----------800-----------------------0.20
Carnations---4000----------------------0.15
Gardenias-----450-----------------------0.25

The florist can either make an economy arrangement selling for \$5.95 or a deluxe arrangement selling for \$14.95. Each economy arrangement contains 3 roses, 2 gardenias, and 10 carnations. Each deluxe arrangement contains 6 roses, 3 gardenias and 15 carnations. All unused flowers are sold at \$0.10 each to a street vendor. Assuming that the florist can sell all the arrangements he can make, find the number of each type of arrangements he should prepare to maximize his profit. (Hint: 5 variables and 3 constraints.) What will be the maximum profit?

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#### Solution Preview

Suppose x is the number of economy arrangement, y is the number of deluxe arrangement. After he sells all the arrangements, he sells
<br>3x+6y roses, 2x+3y gardenias and 10x+15y carnations and earns
<br>5.95x+14.95y dollars.
<br>The total number available for Roses is 800, for Carnations is 4000, ...

#### Solution Summary

Setting up constraints for profit maximization for A florist is planning to make up floral arrangements for the upcoming holiday weekend. He has following supply of flowers in stock this Friday and he cannot get any more.

Type------Number available------Cost per flower

Roses----------800-----------------------0.20
Carnations---4000----------------------0.15
Gardenias-----450-----------------------0.25

The florist can either make an economy arrangement selling for \$5.95 or a deluxe arrangement selling for \$14.95. Each economy arrangement contains 3 roses, 2 gardenias, and 10 carnations. Each deluxe arrangement contains 6 roses, 3 gardenias and 15 carnations. All unused flowers are sold at \$0.10 each to a street vendor. Assuming that the florist can sell all the arrangements he can make, find the number of each type of arrangements he should prepare to maximize his profit. (Hint: 5 variables and 3 constraints.) What will be the maximum profit?

\$2.49