For L. P. P, maximize z=4x1+2x2 subject to 3x1+2x2≥9,x1-x2≤3,x1≥0,x2≥0 has ….

(A) Infinite number of optimal solutions

MHT CET · Maths · Area Under Curves

For L. P. P, maximize $z = 4 x_{1} + 2 x_{2}$ subject to $3 x_{1} + 2 x_{2} \geq 9, x_{1} - x_{2} \leq 3, x_{1} \geq 0, x_{2} \geq 0$ has ….

A Infinite number of optimal solutions
B Unbounded solution
C No solution
D One optimal solution

Verified Solution

Answer & Solution

Correct Answer

(B) Unbounded solution

Step-by-step Solution

Detailed explanation

We have, maximise

z = 4 x_{1} + 2 x_{2}

Subject to constracts,

3 x_{1} + 2 x_{2} \geq 9, x_{1} - x_{2} \leq 3, x_{1} \geq 0, x_{2} \geq 0

On taking given constraints as equation, we get the following graphs

Here, we get feasible region is unbounded.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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