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
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The quantity of column B is greater than quantity of column A The quantity of column A is greater than quantity of column B Both quantities are equal The relationship cannot be determined on the basis of the information supplied |
The quantity of column B is greater than quantity of column A |
Objective function: $Z = 4x + 3y$ Corner points: $(0,0), (0,40), (20,40), (60,20), (60,0)$ Evaluate $Z$ at each corner point: At $(0,0)$: $Z = 4(0) + 3(0) = 0$ At $(0,40)$: $Z = 4(0) + 3(40) = 120$ At $(20,40)$: $Z = 4(20) + 3(40) = 80 + 120 = 200$ At $(60,20)$: $Z = 4(60) + 3(20) = 240 + 60 = 300$ At $(60,0)$: $Z = 4(60) + 3(0) = 240$ Maximum of $Z = 300$ at $(60,20)$ Compare with Column B: 325 Maximum of $Z$ (Column A) = 300 < 325 (Column B) Answer: The quantity of Column B is greater than the quantity of Column A |