Question 23 (4.5 points) Using only the portion of the computer output for a ine

Question

Question 23 (4.5 points) Using only the portion of the computer output for a inear programming probiem presented below, which of the following statements represents a correct inderpredation of the dual price for oonstraint ? Variable XI x2 Value 75 100 Reduced Cost Dual Price 0.25 0.25 Constraint # 1 Slack or Surplus 25 1) If this is a maximization problem the most that the decision maker should be willing to pay for an additional unit of resource one will be 0.25 O 2) For every one unit decrease in the availab ity of resource 1 the objective function value wil' worsen by 0.25 3) All of the above are true. 4) For every one unit increase in the availability of resource 1 the objective function value will improve by 0.25 Save

Explanation / Answer

1) If this is a maximization problem, the most that the decision make should be willing to pay for an additiona unit of resource one will be 0.25

Interpretation of shadow price (or dual price) is such that every one unit change in the constraint brings about a change equivalent to the dual price in the objective function. So For maximization problem, that makes dual price equal to the worth of each additional unit of that resource. However, for minimization problem, this means that objective value will increase with increase in constraint, so that is not a desirable change and hence not an improvement, but worsening

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