# Linear Programming tools

PLEASE EXPLAIN YOUR ANSWERS (why you choose A instead of C, etc.).

C 6. For a resource constraint, either its slack value must be _____ or its shadow price must be ________

a. negative, negative

b. negative, zero

c. zero, zero

d. zero, negative

D 7. For a linear programming problem, assume that a given resource has not been fully used. In other words, the slack value associated with the resource constraint is positive. We can conclude that the shadow price associated with that constraint:

a. will have a positive value

b. will have a negative value

c. will have a value of zero

d. could have a positive, negative or a value of zero. (no sign restrictions)

C 8. Sensitivity analysis is the analysis of the effect of ___________ changes on the _____________

a. price, company

b. cost, production

c. parameter, optimal solution

d. none of the above

C 9. A shadow price reflects which of the following in a maximization problem?

a. the marginal gain in the objective that would be realized by adding 1 unit of a resource

b. the marginal gain in the objective that would be realized by subtracting 1 unit of a resource

c. the marginal cost of adding additional resources

d. none of the above

https://brainmass.com/math/linear-programming/linear-programming-tools-82448

#### Solution Preview

6) c , Slack can only be nonnegative, never negative. The shadow price is "a rate of change" known also as the marginal value of the RHS. The shadow price for nonbinding constraint is always 0.

7) c , ...

#### Solution Summary

The solution contains answers to various problems in linear programming including slack value , shadow price , sensitivity analysis , optimal solution etc.