Problem $1$: SABA toy nlanufacturers make four different types of stuffed animals. The following LP model has been developed for the company.

$\backslash$table$[[$Let$,$X$1=$ Number of stuffed bears$],[$X$2=$ Number of stuffed rabbits,$],[$X$3=$ Number of stuffed dogs,$],[$X$4=$ Number of stuffed cats,$]]$

$\backslash$table$[[$The LP Model,PRODUCTS,,Available,RESOURCES$],[,K1,,x2,,x3,x4,],[$Constraint $1,,3,,1,,1,1,,100,$Stuffing in pounds$],[$Constraint $2,,2,,2,,3,2,,250,$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.