Question 1
Consider the following constraints from a two-variable linear program.
(1) X ≥ 1
(2) Y ≥ 1
(3) X + Y ≤ 9
If these are the only constraints, which of the following points (X, Y) cannot be the optimal solution?
◦ (1, 1)
◦ (4, 4)
◦ (1, 8)
◦ (8, 1)
◦ The question cannot be answered without knowing the objective function.
Question 2
A linear programming maximization problem has been solved. In the optimal solution, two resources are scarce. If an added amount could be found for only one of these resources, how would the optimal solution be changed?
◦ The solution stays the same; the extra resource can't be used without more of the other scarce resource.
◦ The extra resource will cause the value of the objective to rise.
◦ The optimal mix will be rearranged to use the added resource, and the value of the objective function will rise.
◦ The shadow price of the added resource will rise.
◦ The extra resource will cause the value of the objective to fall.
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