CalJuice Company has decided to introduce three fruit juices made from blending
ID: 3108460 • Letter: C
Question
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 required 8 oz each of pineapple and orange juice concentrates. One carton of orange banana juice require 12 oz of range juice concentrate and 4 oz of banana pulp concentrate. Finally, one carton of pineapple-orange-banana juice required 4 oz of pineapple juice concentrate, 8 oz of range juice concentrate, and 4 oz of banana pulp concentrate. The company all so stipulated that the production of pineapple-orange-banana juice should not exceed 620 cartons. Its profit on one carton $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? What is the largest profit it can realize? Are there any concentrates left over? (If so, enter the amount remaining. If not, enter 0.)Explanation / Answer
Let PO = the number of pineapple - orange cartons,
OB = the number of orange - banana cartons,
POB = the number of pineapple - orange - banana cartons
We are maximizing the profit equation
Profit = PO + 0.8 OB + 0.9 POB which can be rewritten as - PO - 0.8 OB - 0.9 POB = 0
The rest of these are constraints which we mentioned in the table like so...
PO OB POB u v w Profit RHS Pineapple 8 0 4 1 0 0 0 16000 Orange 8 12 8 0 1 0 0 24000 Banana 0 4 4 0 0 1 0 5000 limit on PO 0 0 1 0 0 0 0 620 Profit -1 -8 -9 0 0 0 1 0