A ligar programming computer package is needed Georgia Cabinets manufactures chen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for bak and cherry cabinets, the company decided to contract with three maer cabinetmakers to do the final finishing ceration. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete at the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here Cabinetmaker: Cabinetmaker Cabinetmaker) Hours required to completo all the cabinets 10 10 Hour required to completa all the cherry cabinets 60 15 Hours available 40 30 35 Cool per hour $30 43 555 42 For example, Cabinetmaker I estimates at we take 5 hours to complete all the cake cabinets and 8 hours to complete with cherry Cabinets. However, Cabinetmakers only has 40 hour walle for the fire inishing operation. Thus, Cabinetmakers can only complete 40/50 - 0.40.0 80% of the cake cabineta it worked only on a cabinets. Similarly, Cabinetmaker I can only complete 40/60 0.87, or 67% of the cherry Cabinets I worked only on cherry cabinet (a) formulate a linear programming model that can be used to determine the percentage of the cabinets and the percentage of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimise the total cost of completing both projects (tol gercentage of the cabinetseigned to cabinetmaker 1, 2-percentage of oak cabinets signed to cabinetmaker 2,0 percentage of oak cabinetsised to cabinetmaker 3, C1-percentage of cherry cabinets assigned to cabinetmaker 1. percentage of cherry Cabinets egned to cabinetmaker and percentage of cherry cabinets assigned to cabinetmaker 33 hours available hours available hours available 01, 03, 01, CIC, the model formulated in ter what percentage of the sak cabinet and what percentage the cherry cabinets could be red to each catater what is the total cost on coming both prejectat (Hard your percept value to the decimale) ci 02 09 CH 2 (C) If Cabinetmaker 1 hes additional hours available, would the optimal solution change? Explain. Yes, each additional hour of time for cabinetmaker I will reduce the total cost by $-1.75 per hour. Yes, each additional hour of time for cabinetmaker I will reduce the total cost by $5 per hour. No, cabinetmaker 1 has a slack of 26.458 hours, so increasing cabinetmaker 1's time will not reduce costs. No, cabinetmaker I has a slack of 37.5 hours, so increasing cabinetmaker I's time will not reduce costs. (d) If Cabinetmaker 2 has additional hours available, would the optimal solution change? Explain. Yes, each additional hour of time for cabinetmaker 2 will reduce the total cost by 5-1.75 per hour. Yes, each additional hour of time for cabinetmaker 2 will reduce the total cost by $5 per hour. No, cabinetmaker 2 has a slack 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 cabinetmaker 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 optimal solution? Explain The new objective function coefficients for 02 and Care and . respectively. The optimal solution Seed and has a value of $ A ligar programming computer package is needed Georgia Cabinets manufactures chen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for bak and cherry cabinets, the company decided to contract with three maer cabinetmakers to do the final finishing ceration. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete at the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here Cabinetmaker: Cabinetmaker Cabinetmaker) Hours required to completo all the cabinets 10 10 Hour required to completa all the cherry cabinets 60 15 Hours available 40 30 35 Cool per hour $30 43 555 42 For example, Cabinetmaker I estimates at we take 5 hours to complete all the cake cabinets and 8 hours to complete with cherry Cabinets. However, Cabinetmakers only has 40 hour walle for the fire inishing operation. Thus, Cabinetmakers can only complete 40/50 - 0.40.0 80% of the cake cabineta it worked only on a cabinets. Similarly, Cabinetmaker I can only complete 40/60 0.87, or 67% of the cherry Cabinets I worked only on cherry cabinet (a) formulate a linear programming model that can be used to determine the percentage of the cabinets and the percentage of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimise the total cost of completing both projects (tol gercentage of the cabinetseigned to cabinetmaker 1, 2-percentage of oak cabinets signed to cabinetmaker 2,0 percentage of oak cabinetsised to cabinetmaker 3, C1-percentage of cherry cabinets assigned to cabinetmaker 1. percentage of cherry Cabinets egned to cabinetmaker and percentage of cherry cabinets assigned to cabinetmaker 33 hours available hours available hours available 01, 03, 01, CIC, the model formulated in ter what percentage of the sak cabinet and what percentage the cherry cabinets could be red to each catater what is the total cost on coming both prejectat (Hard your percept value to the decimale) ci 02 09 CH 2 (C) If Cabinetmaker 1 hes additional hours available, would the optimal solution change? Explain. Yes, each additional hour of time for cabinetmaker I will reduce the total cost by $-1.75 per hour. Yes, each additional hour of time for cabinetmaker I will reduce the total cost by $5 per hour. No, cabinetmaker 1 has a slack of 26.458 hours, so increasing cabinetmaker 1's time will not reduce costs. No, cabinetmaker I has a slack of 37.5 hours, so increasing cabinetmaker I's time will not reduce costs. (d) If Cabinetmaker 2 has additional hours available, would the optimal solution change? Explain. Yes, each additional hour of time for cabinetmaker 2 will reduce the total cost by 5-1.75 per hour. Yes, each additional hour of time for cabinetmaker 2 will reduce the total cost by $5 per hour. No, cabinetmaker 2 has a slack 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 cabinetmaker 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 optimal solution? Explain The new objective function coefficients for 02 and Care and . respectively. The optimal solution Seed and has a value of $