problem 26 please

local dealers throughout do the final finishing opera does the shadow price associated with all that would occur from this increased rate of return? 25. Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers thro the Southeast. Because of a large backlog of orders for onk and cherry cabinets, the pany decided to contract with three smaller cabinetmakers to do the final finishing tion. For the three cabinetmakers, the number of hours required to complete all the cabinets, the number of hours required to complete all the cherry cabinets, the number hours available for the final finishing operation, and the cost per hour to perform the wo are shown here: Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 60 Hours required to complete all the oak cabinets Hours required to complete all the cherry cabinets Hours available Cost per hour 40 30 $36 $42 For example, Cabinetmaker l estimates that it will take 50 hours to complete all the cak cabinets and 60 hours to complete all the cherry cabinets. However, Cabinetmaker I only has 40 hours available for the final finishing operation. Thus, Cabinetmaker I can only complete 40/50 - 0.80, or 80% of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker I 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. 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 of completing both projects? c. If Cabinetmaker 1 has additional hours available, would the optimal solution change? Explain. d. If Cabinetmaker 2 has additional hours available, would the optimal solution change? Explain. e. Suppose Cabinetmaker 2 reduced its cost to $38 per hour. What effect would this change have on the optimal solution? Explain. 26. Benson Electronics manufactures three components used to produce cell phones and other communication devices. In a given production period, demand for the three components may exceed Benson's manufacturing capacity. In this case, the company meets demand by purchasing the components from another manufacturer at an increased cost per unit Problems 351 Benson's manufacturing cost per unit and purchasing cost per unit for the three compo- nents are as follows Source Manufacture Purchase Component 1 $4.50 S6.50 Component 2 $5.00 $8.80 Component 3 $2.75 $7.00 Manufacturing times in minutes per unit for Benson's three departments are as follows: Componenti Component 2 Component 3 Department Production Assembly Testing & Packaging For instance, each unit of component I that Benson manufactures requires 2 minutes of duction time, I minute of assembly time, and 1.5 minutes of testing and packaging time. For the next production period, Benson has capacities of 300 hours in the production department 20 hours in the assembly department, and 300 hours in the testing and packaging department formulate a linear programming model that can be used to determine how many units of each component to manufacture and how many units of each component to nurchase. Assume that component demands that must be satisfied are 6000 units for component 1,4000 units for component 2, and 3500 units for component 3. The chien tive is to minimize the total manufacturing and purchasing costs, h What is the optimal solution? How many units of each component should be man factured and how many units of each component should be purchased? Which departments are limiting Benson's manufacturing quantities? Use the shadow orice in determine the value of an extra hour in each of these departments Sunse that Benson had to obtain one additional unit of component 2. Discuss what ahe shadow price for the component 2 constraint tells us about the cost to obtain the additional unit. la can be harvested using either a "wet" method ora "dry" method, Dry-harvested Cranberries can be harvested using either a "wet" m harvins can be sold at a premium, while wet-harvested cranberries are used mainly mind bring in less revenue. Fresh Made Cranberry Cooperative must decide cranberry juice and bring in less revenue. Fresh Made C ch of its cranberry crop should be harvested wet and how much should be dry her d esh Made has 5000 harrels of cranberries that can be harvested using elibsih hacia el for 2 yr himmelendut 27