Linear Programing Practice Questions:

Answer the following questions based on the given sensitivity report for a profit

maximization linear program:

Variable Cells Table:

$1)$ What is the optimal value of the decision variables $($i$.$e$.,$ optimal number of widgets

and gadgets produced$)?$

$2)$ What is the optimal profit value?

$3)$ What should the objective coefficient $($unit profit value$)$ of gadgets be greater than

so that it becomes optimal to produce gadgets?

$4)$ Are the following statements true or false?

a$.$ It$$ll still be optimal to produce the same number of widgets and gadgets if the

objective coefficient $($unit profit value$)$ of widgets is lowered from $$2\mathrm{.}25$ to

$$1\mathrm{.}25.$

b$.$ It$$ll still be optimal to produce the same number of widgets and gadgets if the

objective coefficient $($unit profit value$)$ of gadgets is lowered from $$2\mathrm{.}60$ to

$$1\mathrm{.}25.$

Constraints Table:

$5)$ Identify the binding and the nonbinding constraint.

$6)$ What is the slack for the wood constraint? What is the shadow price for this

constraint?

$7)$ If an additional unit of labor resource is available how much would the optimal profit

value increase? What if $100$ more units of labor hours are available, how much

would the optimal profit increase now?

$8)$ Are the following statements true or false?

a$.$ If we have an additional $100$ units of wood available, the optimal profit will go

up by $$1125.$

b$.$ If we have an additional $10000$ units of labor hours available, we can$$t say

how much the profit would increase from looking at the given sensitivity

report.