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a Outside the feasible space. b No solution.

a Outside the feasible space. b No solution.

A is added, the firm can increase total profit by $1.50. It would increase profits to buy additional units of input A at any price less than $1.50 per unit, at least up until the point at which A is no longer a binding constraint. This assumes that the cost of input A is currently fixed. If those costs are variable, the firm would be willing to pay $1.50 above the current price of input A to eliminate this constraint. Because availability of B also imposes an effective constraint, the firm can also afford to pay up to $6 for a marginal unit of B.

Finally, both dual slack variables equal zero at the optimal solution. This means that the implicit value of resources required to produce a single unit of X or Y is exactly equal to the profit contribution provided. The opportunity cost of producing X and Y is zero, meaning that the resources required for their production are not more valuable in some alternative use. This is consistent with the primal solution, because both X and Y are produced at the optimal solution. Any product with a positive opportunity cost is suboptimal and would not be produced.

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