Practice set$-$Lecture $2$ LP sensitivity

A constraint with a positive slack value

a$.$ will have a positive shadow price.

b$.$ will have a negative shadow price.

c$.$ will have a shadow price of zero.

d$.$ has no restrictions for its shadow price.

Sensitivity analysis information in computer output is based on the assumption of

a$.$ no coefficient changes.

b$.$ one coefficient changes.

c$.$ two coefficients change.

d$.$ all coefficients change.

When the cost of a resource is sunk, then the shadow price can be interpreted as the

a$.$ minimum amount the firm should be willing to pay for one additional unit of the resource.

b$.$ maximum amount the firm should be willing to pay for one additional unit of the resource.

c$.$ minimum amount the firm should be willing to pay for multiple additional units of the resource.

d$.$ maximum amount the firm should be willing to pay for multiple additional units of the resource.

Which of the following is not a question answered by sensitivity analysis?

a$.$ If the right$-$hand side value of a constraint changes, will the objective function value change?

b$.$ Over what range can a constraint's right$-$hand side value without the constraint's shadow price possibly changing?

c$.$ By how much will the objective function value change if the right$-$hand side value of a constraint changes beyond the range of sensitivity$?$

d$.$ By how much will the objective function value change if a decision variable's coefficient in the objective function changes within the range of sensitivity$?$

For a maximization problem, assume that a constraint is binding. If the original amount of a resource is $4lbs.$ and the range of feasibility $($sensitivity range$)$ for this constraint is from $3lbs.$ to $6lbs,$ increasing the amount of this resource by $1lb.$ will result in the

a$.$ same product mix, different total profit.

b$.$ different product mix, same total profit as before.

c$.$ same product mix, same total profit.

d$.$ different product mix, different total profit.

A plant manager is attempting to determine the production schedule of various products to maximize profit. Assume that a machine hour constraint is binding. If the original amount of