$\backslash$table$[[$Let$,x1=$ Number of stuffed bears,,,,,$],[x2=$ Number of stuffed rabbits,,,,,$],[x3=$ Number of stuffed dogs,,,,,$],[x4=$ Number of stuffed cats,,,,,$],[$The LP Model,PRODUCTS,,,$],[,,],[$Constraint $1,3,1,,1,,7,,\backslash$table$[[$Available$],[100]],\backslash$table$[[$RESOURCES$],[$Stuffing in pounds$]]],[$Constraint $2,2,2,,3,,,,\frac{100}{250},$Yards of fabric$],[$Constraint $3,4,2,,1,,2,,300,$Assembly time in hours$],[$Constraint $4,1,4,,2,,3,,200,$Pieces of trim$],[$Profit$/$unit$,8\mathrm{.}00,5\mathrm{.}00,$$$,6\mathrm{.}00,$$$,4\mathrm{.}00,,,]]$

a$.$ Solve the above Linear programming problem and obtain sensitivity analysis.

DO NOT CHANGE ANY OF THE UNITS

Use your sensitivity output to answer the following questions.

b$.$ Which constraints are$($is$)$ non$-$binding and what does it mean?

c$.$ If the profit per unit of stuffed rabbits is increased by $$2,$ will the optimal solution change?

What would be the new value of the objective function? Give the new value here

d$.$ As you note, at optimum no stuffed cats $(x4)$ are being produces.

What should the profit per unit of stuffed cats $($X$4),$ so it becomes profitable to produce it$?$ Explain how you arrived at the value.

e$.$ Fifty yards of fabric can be obtained at $1\mathrm{.}20$ above the current cost.

Should the additional yards of fabric be obtained at the quoted cost? Why or why not? Fully explain.