1) CalJuice Company has decided to introduce three fruit juices made from blending two or more concentrates. These juices will be packaged in 2-qt (64-oz) cartons. One carton of pineapple-orange juice requires 8 oz each of pineapple and orange juice concentrates. One carton of orange-banana juice requires 12 oz of orange juice concentrate and 4 oz of banana pulp concentrate. Finally, one carton of pineapple-orange-banana juice requires 4 oz of pineapple juice concentrate, 8 oz of orange juice concentrate, and 4 oz of banana pulp concentrate. The company has decided to allot 16,000 oz of pineapple juice concentrate, 24,000 oz of orange juice concentrate, and 5000 oz of banana pulp concentrate for the initial production run. The company also stipulated that the production of pineapple-orange-banana juice should not exceed 800 cartons. Its profit on one carton of pineapple-orange juice is $1.00, its profit on one carton of orange-banana juice is $0.80, and its profit on one carton of pineapple-orange-banana juice is $0.90. To realize a maximum profit, how many cartons of each blend should the company produce?
pineapple-orange juice cartons
orange-banana juice cartons
pineapple-orange-banana juice cartons
What is the largest profit it can realize?
Are there any concentrates left over? (If so, enter the amount remaining. If not, enter 0.)
pineapple concentrate oz
orange concentrate oz
banana pulp concentrate oz
2)Solve the linear programming problem by the simplex method.
P = x + 4y ? 2z
3x + y ? z ? 92
2x + y ? z ? 46
?x + y + z ? 92
x ? 0, y ? 0, z ? 0
what is p & x,y,z
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