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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
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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