This Course related to Quantitative Methods in Engineering Management.Please solve it step by step to understand it$.$ Thank you.Problem $1.$ For each question, choose the most appropriate answer from the options provided. If

you select 'False,$\text{'}$ provide a brief explanation of your reasoning. $(20$pts$)$

Q$1.$ Assume you have to allocate funds to different departments, the objective function and

constraints are linear, the parameters are known for certain, and the allocation variables, $x_{\text{d}\text{e}\text{p}},$ are

divisible, where dollar positive value assigned to $x_{\text{d}\text{e}\text{p}}$ means fund allocation to department dep,

and negative value of $x_{\text{d}\text{e}\text{p}}$ means defunding or fund withdrawal of department dep. Is this an LP

problem?

A$)$ True.

B$)$ False.

Q$2.$ Is the following problem an LP$?$

Maximize Profit $=$$$40x_1+$$$20x_2+$$$30x_3-$$$100x_4$

A$)$ True.

B$)$ False.

Q$3.$ In the corner point method, it is paramount to evaluate the $(0,0)$ corner point, assuming it is a

feasible point.

A$)$ True.

B$)$ False.

Q$4.$ Infeasibility is a special case that happens when the decision$-$maker is unsatisfied with the

feasible region.

A$)$ True.

B$)$ False.

Q$5.$ Unboundedness is a special case that happens when there is a trillion feasible solution to an

LP problem.

A$)$ True.

B$)$ False.

Q$6.$ The shadow price of a non$-$binding constraint is always zero.

A$)$ True.

B$)$ False.

Q$7.$ Sensitivity analysis finds range of contrib. rates, where the feasible area remains unchanged.

A$)$ True.

B$)$ False.

Q$8.$ Sensitivity analysis finds range of RHS values, where current solution remains unchanged.

A$)$ True.

B$)$ False.

Q$9.$ Any decision point along the Iso$-$Profit line will yield the same profit value.

A$)$ True.

B$)$ False.

Q$10.$ The optimal solution for an LP$,$ will never appear in the middle of the feasible region.