linear programming computer package is needed. Seorgla Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation, For the three cabinetmakers, the number of hours required to comple il the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours avallable for the final finishing operation, and the cost per hour 0 perform the work are shown here. For example, Cabinetmaker 1 estimates it will take 50 hours to complete all the oak cabinets and 60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 . only has 40 hours avaliable for the final finishing operation. Thus, Cabinetmaker 1 can only complete 40/50=0.80, or 80%, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 40/60=0.67, or 67%, of the cherry cabinets if it worked only on cherry cabinets. (a) Formulate a linear programming model that can be used to determine the percentage of the oak cabinets and the percentage of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimize the total cost of completing both projects. (Let or = percentage of oak cabinets assigned to cabinetmaker 1,02 = percentage of oak cabinets assigned to cabinetmaker 2,03= percentage of oak cabinets asianed to cabinetmaker 3,Cl= percentage of cherry cabinets assigned to cablinetmaker 1,C2= percentage of cherry cabinets assigned to cablnetmaker 2 , and C3= percentage of cherry cabinets assigned to cabinotmaket 3.) Min Check which yariable(s) sbould be in your answer. s.t. hours available 1 Chock whilet varbobie(c) should be in your answer bours avaloble 2 hours avaitabie 1 oak alery 01,02,03,Cl1,Cl2,a0 (b) Solve the model formulated in part (a). What percentage of the oak cabinets and what percentage of the cherry cabinets should be assigned to each cabinetmaker? What is the total cost (in s) of completing both projects? (Round your percentage values to one decimal place.) (c) If Cabinetmaker 1 hus addational hours available, nould the optimal solotion change? Explain. Yes, each additional hour of time for cabinetmaker 1 will reduce the total cost by $1.75 per heul. Mes, wach additional hour of time for cabinetmaker 1 will reduce the total cost by $5 per hour No, cablhetmaker 1 has a slack of 26,456 hours, so increasing cabisetmaker 1 's time will not reduce coste. No, cabinetmaker 2 has a slack of 37.5 hours, fo increasing cabinetmuker 1 's time will not reduce costs. (d) If Cabinetmaker 2 fas addatenal hours arailable, would the eptimal solution change? Explain. res; each additionat hour of time for cabinetmaker 2 wal redoce the total cost by \$-1.75 per hour. Yes, each additional hour of time for cabinetmaker 2 will reduce the total cout by $5 per hoir. No, cabinetmaker 2 has a stack of 26.458 hours, so increasing cabinetmaker 2 's time will not reduce costs. No, cabinetmaker 2 has a slack of 37.5 hours, so increasing catinetmaker 2 's time will not reduce costs. (e) Suppose Cabinetmaker 2 reduced its cost to $38 per hour. What effect would this change have on the eptimal solution? Explain. The new objective function coefficients for O2 and C2 are of 5 and - respectively. The optimal solution and has a value