CalJuice Company has decided to introduce three fruit juices made from blending
ID: 3196634 • 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 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 620 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? What is the largest profit it can realize? Are there any concentrates left over?
Explanation / Answer
Variables
no. carton of Pineapple and orange = a
no. carton of banana and orange = b
no. carton of Pineapple and orange and banana = c
Constraints
1. a,b and c are non-negative integers
2. max pineapple juice concentrate is 16000, so 8a+4c <= 16000
3. max orange juice concentrate is 24000, so 8a+12+8c <= 24000
4. max banana pulp concentrate is 5000, so 4b+4c <= 5000
5. c <= 680
objective
maximize profit = 1a+0.8b+0.9c
solution
answer is
only banana pulp concentrate left 520 oz.
rest all consumed totally
maximum profit = 2624.
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cartons 1 carton total variable optimal pineapple orange banana profit pineapple orange banana profit a 1660 8 8 0 1 13280 13280 0 1660 b 440 0 12 4 0.8 0 5280 1760 352 c 680 4 8 4 0.9 2720 5440 2720 612 total 16000 24000 4480 2624 constraint 16000 24000 5000 check 0 0 520 constrain2 0