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Formulate but Do Not Solve the Following Exercise as a Linear

question 19

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Formulate but do not solve the following exercise as a linear programming problem.
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 fluid-oz) cartons. To make one carton of pineapple-orange juice requires 7 oz each of pineapple and orange juice concentrates. To make one carton of orange-banana juice requires 12 oz of orange juice concentrate and 4 oz of banana pulp concentrate. Finally, to make one carton of pineapple-orange-banana juice requires 5 oz of pineapple juice concentrate, 6 oz of orange juice concentrate, and 3 oz of banana pulp. The company has decided to allot 16,000 oz of pineapple juice concentrate, 25,000 oz of orange juice concentrate, and 3,000 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 500 cartons. Its profit on one carton of pineapple-orange juice is $1.10; its profit on one carton of orange-banana juice is $0.90, and its profit on one carton of pineapple-orange-banana juice is $0.80. To realize a maximum profit, how many cartons of each blend should the company produce?

Definitions:

Feelings of Inferiority

Emotions experienced when an individual perceives themselves to be lesser or not as competent as others, often leading to motivation to overcome such feelings by striving for achievement.

Adler

Refers to Alfred Adler, a psychologist known for introducing concepts such as the inferiority complex and the importance of social context in personality development.

Genital Stage

In Freudian psychoanalysis, the final stage of psychosexual development, occurring from puberty onward, focused on mature sexual intimacy and pleasure.

Puberty

The developmental stage in humans marking the onset of adolescence, characterized by physical and hormonal changes that lead to sexual maturity.