$\backslash$table$[[,$Resource Requirements$],[,$Wood $($Ib$),$Upholstery $($yd$),$Labor $($hr$),$Budget $($$$)],[$Sofa$,3,6,3,30],[$Cabinet$,3,0,4,50],[$Chair$,2,3,2,10],[$Total Available Resources,$1125,500,625,5200]]$

Due to a previous order, the company is required to produce at least $120$ chairs. Each sofa earns $$200$ in profit, each cabinet, $$160,$ and each chair, $$150.$

The company wants to know how many pieces of each type of furniture to make per week to maximize profit. Linear programming $($LP$)$ model of this problem is given as follows:

Maximize $200x+160y+150z$

$s.t.3x+3y+2z1125$

$,6x+3z500$

$,3x+4y+2z625$

$,30x+50y+10z5200$

$,z120$

$,x,y,z0$

Solving the above LP model using Excel solver gives the following results:

$1$

Variable Cells

$\backslash$table$[[,,$Final,,,,$],[$Cell$,$Name,Reduced,$\backslash$table$[[$Objective$],[$Coefficient$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]],],[$$B$$11,$Decision Var. Sofa,$0,-132,200,132,1E+30$