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?