Calculate the shadow price for Fries.

Make sure your answer is accurate to two decimal places.

Question

Calculate the shadow price for Fries.

Make sure your answer is accurate to two decimal places.

BlackTom AI · Accepted Answer

Shadow price, in optimization and linear programming, represents the rate at which the objective value would improve if you could increase the right-hand side (RHS) of a constraint by one unit. In other words, it is the dual value associated with a constraint.

To compute it, you typically:
- Solve the primal problem and examine the optimal solution.
- Look at the corresponding dual problem or at the sensitivity analysis results from the solver.
- Identify the dual value (shadow price) for the constraint of interest. This value tells you how much the objective would change per one-unit increase in that constraint's RHS, holding all else constant.

Since the provided answer for the shadow price of Fries is 0.04, the interpretation would be: increasing the RHS of the relevant constraint by one unit would improve (or decrease, depending on the sign convention) the objective by 0.04 units. In practical terms, if the objective is profit, a one-unit relaxation of the constraint would raise profit by 0.04.

Note that shadow prices are valid within the range of stability (the allowable increase/decrease) for which the basis of the optimal solution does not change. If you increase the RHS beyond that range, the shadow price may change and a new sensitivity analysis would be required.

If you have the original LP data (objective, constraints, and RHS), I can walk you through computing the shadow price step by step from scratch and verify the result numerically.

COMM_V 190 101-104 2025W1 Practice Midterm

Calculate the shadow price for Fries. Make sure your answer is accurate to two decimal places.

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