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Question
The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y ______.
Compare the quantity in Column A and Column B
| Column A | Column B |
| Maximum of Z | 325 |
Options
The quantity in column A is greater
The quantity in column B is greater
The two quantities are equal
The relationship can not be determined on the basis of the information supplied
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Solution
The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y the quantity in column B is greater.
Compare the quantity in Column A and Column B
| Column A | Column B |
| Maximum of Z | 325 |
Explanation:
| Corner points | Value of Z = 4x + 3y | |
| (0, 0) | Z = 0 | |
| (0, 40) | Z = 0 + 3(40) = 120 | |
| (20, 40) | Z = 4(20) + 3(40) = 200 | |
| (60, 20) | Z = 4(60) + 3(20) = 300 | → Maximum |
| (60, 0) | Z = 4(60) + 3(0) = 240 |
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