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Concept explainers
Explanation of Solution
Formulation of a Linear
Let “xij” 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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Chapter 3 Solutions
Operations Research : Applications and Algorithms
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- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
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