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 |
Answer & explanation
Correct answer: option 1
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