Consider the following linear programming problem with two decision variables \(x_1\) and \(x_2\). There are three constraints involving resources \(R_1, R_2\) and \(R_3\) as indicated.
Maximize \(Z = 6x_1+5x_2\)
Subject to
\(2x_1+5x_2\leq 40\) \(R_1\)
\(2x_1 + x_2 \leq 22\) \(R_2\)
\(x_1 + x_2 \leq 13 \) \(R_3\)
\(X_1 \geq0, \ X_2 \geq 0\)
The optimal solution of the problem is: \(x_1 =9\) and \(x_2=4\)
For which one of the following options, the shadow price of the resource(s) will have non-zero value(s)?
Maximize \(Z = 6x_1+5x_2\)
Subject to
\(2x_1+5x_2\leq 40\) \(R_1\)
\(2x_1 + x_2 \leq 22\) \(R_2\)
\(x_1 + x_2 \leq 13 \) \(R_3\)
\(X_1 \geq0, \ X_2 \geq 0\)
The optimal solution of the problem is: \(x_1 =9\) and \(x_2=4\)
For which one of the following options, the shadow price of the resource(s) will have non-zero value(s)?
- R1, R2 and R3
- R1 and R2
- R2 and R3
- R1 only
The Correct Option is C
Solution and Explanation
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