CalJuice Company has decided to introduce three fruite juices made from blending
ID: 2751660 • Letter: C
Question
CalJuice Company has decided to introduce three fruite 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 od pineapple juice concentrate, 8 oz of orange juice concentrate, and 4 oz of banana pulp. 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 has also stipulated that the production of pinapple-orange-banana juice should not exceed 800 cartons. Its profit on one carton of pineapple-orange juice is $1.00, its profic on one carton of orange-banana juice is $0.80, and its profit on one cart of pineapple-orange-banana juice is $0.90. To realize the 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
Let the number of pineapple-orange juice carton be = X
Let the number of orange-banana juice carton be = Y
Let the number of orange-pineapple-banana juice carton be = Z
Equations are:-
1. Z <= 800
2. $ 1X + $0.8Y + $0.90Z = Maximum
3. 8X + 4Z <= 16000
4. 8X + 12Y + 8Z <= 24000
5. 4Y + 4Z <=5000
Let Z= 800
Then from
1. We get X = 1525 units
2. We get Z = 800 units
3. We get Y = 450 units
Maximum profit on this is $ 2,605.
Concentrates left over = 600 oz of Pineapple as after 800 units of pineapple-orange-banana will consume 3200 oz of pineapple & banana each and 6400 oz of orange. 450 cartons of orange-banana will consume 450oz of orange and banana each. 1525 cartons of pineapple-orange will consure 12200 oz of pienapple and orange each.