Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Linear Programming

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 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

Correct Answer:

The quantity of column B is greater than quantity of column A

Explanation:

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