Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Hours required to complete all the oak cabinets 17 10 32 Hours required to complete all the cherry cabinets Hours available Cost per hour 60 43 36 40 25 30 $38 $42 $54 For example, Cabinetmaker 1 estimates that it will take 47 hours to complete all the oak cabinets and 60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 40/47 -0.85, or 85%, 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 proportion of the oak cabinets and the proportion 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 O₁ - proportion of Oak cabinets assigned to cabinetmaker 1 Os O2 = proportion of Oak cabinets assigned to cabinetmaker 2 proportion of Oak cabinets assigned to cabinetmaker 3 C₁ = proportion of Cherry cabinets assigned to cabinetmaker 1 C₂-proportion of Cherry cabinets assigned to cabinetmaker 2 C₁ = proportion of Cherry cabinets assigned to cabinetmaker 3 Min s.t. 01 + 02 + 01 03 + C Cal+ Ca 0 01 + O₂+ 0 CL C₂ + C: + C3 Hours avail. 11 Hours avail. 2 Hours avail. 3 Oak Cherry 01, 02, 03, C1, C2, C3 20 b. Solve the model formulated in part (a). What proportion of the oak cabinets and what proportion of the cherry cabinets should be assigned to each cabinetmaker? What is the total cost of completing both projects? If required, round your answers for the proportions to three decimal places, and for the total cost to two decimal places. b. Solve the model formulated in part (a). What proportion of the oak cabinets and what proportion of the cherry cabinets should be assigned to each cabinetmaker? What is the total cost of completing both projects? If required, round your answers for the proportions to three decimal places, and for the total cost to two decimal places. Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Oak Os- Cherry C₁ = C₂ = C₁ Total Cost - $ c. If Cabinetmaker 1 has additional hours available, would the optimal solution change? Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. d. If Cabinetmaker 2 has additional hours available, would the optimal solution change? e. Suppose Cabinetmaker 2 reduced its cost to $39 per hour. What effect would this change have on the optimal solution? If required, round your answers for the proportions to three decimal places, and for the total cost to two decimal places. Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Oak Cherry C₁ = C₂ = Ca= Total Cost = $