Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec's production schedule calls for 5000 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown. Component Frame Support Strap Manufacturing Cost $38.00 Purchase Cost $51.00 $11.50 $15.00 $ 6.50 $ 7.50 Three departments are involved in the production of these components. The time (in min- utes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows: Component Frame Support Strap Capacity (hours) Department Cutting Milling Shaping 3.5 2.2 3.1 1.3 1.7 2.6 0.8 1.7 350 420 680 a. Formulate and solve a linear programming model for this make-or-buy application. How many of each component should be manufactured and how many should be purchased? b. What is the total cost of the manufacturing and purchasing plan? c. How many hours of production time are used in each department? e. Another manufacturer has offered to sell frames to Frandec for $45 each. Could Fran- dec improve its position by pursuing this opportunity? Why or why not? The Silver Star Bicycle Company will be manufacturing both men's and women's models of its Easy-Pedal bicycles during the next two months. Management wants to develop a production schedule indicating how many bicycles of each model should be produced in each month. Current demand forecasts call for 150 men's and 125 women's models to be shipped during the first month and 200 men's and 150 women's models to be shipped during the second month. Additional data are shown: Production Model Men's Women's Costs Labor Requirements (hours) Manufacturing Current Assembly Inventory $120 2.0 1.5 20 $ 90 1.6 1.0 30 Last month the company used a total of 1000 hours of labor. The company's labor relations policy will not allow the combined total hours of labor (manufacturing plus assembly) to increase or decrease by more than 100 hours from month to month. In addition, the company charges monthly inventory at the rate of 2% of the production cost based on the inventory levels at the end of the month. The company would like to have at least 25 units of each model in inventory at the end of the two months. a. Establish a production schedule that minimizes production and inventory costs and satisfies the labor-smoothing, demand, and inventory requirements. What inventories will be maintained, and what are the monthly labor requirements? b. If the company changed the constraints so that monthly labor increases and decreases could not exceed 50 hours, what would happen to the production schedule? How much will the cost increase? What would you recommend?