Consider the production problem: Find the shadow price for resource 2. Identify the binding and nonbinding constraints.
A) The shadow price for resource 2 is $60 .Constraints 1, 2 and 3 are binding constraints.
B) The shadow price for resource 2 is $0.1 .Constraints 1 and 2 are binding constraints and constraint 3 is nonbinding.
C) The shadow price for resource 2 is $60 .Constraints 1 and 3 are nonbinding constraints and constraint 2 is binding.
D) The shadow price for resource 2 is $0.1 .Constraint 1 is binding constraint and constraints 2 and 3 are nonbinding.

Question

Consider the production problem:  Find the shadow price for resource 2. Identify the binding and nonbinding constraints.
A) The shadow price for resource 2 is $60 .Constraints 1, 2 and 3 are binding constraints. 
B) The shadow price for resource 2 is $0.1 .Constraints 1 and 2 are binding constraints and constraint 3 is nonbinding. 
C) The shadow price for resource 2 is $60 .Constraints 1 and 3 are nonbinding constraints and constraint 2 is binding. 
D) The shadow price for resource 2 is $0.1 .Constraint 1 is binding constraint and constraints 2 and 3 are nonbinding.

Quizplus · Accepted Answer

To find the shadow price for resource 2, we need to perform sensitivity analysis and solve the problem again by incrementing resource 2's availability by 1 unit and observe the change in the objective function value. Here, after incrementing resource 2's availability by 1 unit, the objective function value increases by $6, indicating that resource 2 is binding.
Therefore, the shadow price for resource 2 is the amount by which the objective function value increases per unit increase in resource 2's availability, which is $6/60 = $0.1. 
From the original problem, we can see that constraints 1 and 2 involve resource 2, and after solving the problem, we obtain slack values of 0 for both of these constraints, indicating that they are binding constraints. Constraint 3 does not involve resource 2, and the slack value of 50 indicates that it is a nonbinding constraint.

Consider the Production Problem: Find the Shadow Price for Resource