Formulation of a Linear Programming (LP) to help O.J. maximize the profit:

Let “x_ij” be the number of pounds of grade “i” oranges used in product from “j”.

Let grade 1 stand for grade 6 oranges, and 2 for grade 9 oranges.

The objective of function is to maximize the profit of O.J. Juice Company.

Total number of pounds of oranges sold in bag is x11+x21, and total number of pounds of oranges sold as juice is x21+x22

cost of orange in bag = revenue−variable cost=(0.5−0.2)(x11+x21)=0.3(x11+x21)cost of orange as juice = revenue−variable cost=(1.5−1.05)(x12+x22)=0.45(x12+x22)

Therefore, the objective of the function is,

Maximize z = 0.3(x11+x21)+0.45(x12+x22)

Constraint 1:

The company has total 120000 lb of grade 6 oranges.

grade 9 orange in bag + grade 9 orange in juice ≤ 120000x11+x12≤120000

Constraint 2:

The company has total 100000 lb of grade 9 oranges.

grade 9 orange in bag + grade 9 orange in juice ≤ 120000x11+x12≤120000

Constraint 3:

Total quality of the oranges in the bag is,

6x11+9x21x11+x21

This should be greater than or equal to 7

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Operations Research : Applications and Algorithms

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