$(2)Whatis$ the optimal plan for tire production? $(Provide$ the solution values $of$ the decision variables.$)Whatis$ the Total Cost $of$ this plan?

$(3)Oneof$ the workers $is$ planning $to$ take $100hoursof$ unpaid vacation I April. What would $be$ the impact $on$ the objective function value $(Total$ Cost$)if$ his vacation plan $is$ approved? $(Usesensitivity$ analysis $to$ determine. Show your work.$)$

$(4)Insteadof$ taking the vacation $in$ April, the worker $in$ question #$3wantsto$ take his vacation $in$ June. What $is$ the impact $on$ the objective function value $(Total$ Cost$)if$ his vacation $is$ approved for June?

$(5)The$ time $it$ takes $to$ assemble $an$ Invincible tire will increase from $1\mathrm{.}5hoursto1\mathrm{.}64hours$ beginning $in$ June due $toare-$engineering $of$ the assembly process causing $an$ increase $in$ the per unit production cost $of$ the tire from $$8\mathrm{.}25(1\mathrm{.}5hrs.x$$$5\mathrm{.}50)to$ approximately $$9\mathrm{.}00.What$ effect, $if$ any, will this have $on$ the objective function value $(Total$ Cost$)?(THISIS$ A CHALLENGE QUESTION!$)$

Nonnegativity restrictions: all $x_{ij},l_{ij}0$ for all $ofi,j$ SPARTAN GLORY TIRE PRODUCTION PLANNING PROBLEM

DECISION VARIABLES $OF$ THE LINEARY PROGRAMMING MODEL

PROBLEM INPUT DATA $(MODEL$ PARAMETERS$)$