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- A small firm makes three similar products, which all follow the same three-step process, consisting of milling, inspection, and drilling. Product A requires 12 minutes of milling, 5 minutes forinspection, and 10 minutes of drilling per unit; product B requires 10 minutes of milling, 4 minutesfor inspection, and 8 minutes of drilling per unit; and product C requires 8 minutes of milling, 4minutes for inspection, and 16 minutes of drilling. The department has 20 hours available duringthe next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes$2.40 per unit to profit, product B contributes $2.50 per unit, and product C contributes $3.00 perunit. Determine the optimal mix of products in terms of maximizing contribution to profits for theperiod. Then, find the range of optimality for the profit coefficient of each variable.Dalton Desk makes two different types children's desks: a regular model (R) and a deluxe model (D) with an extra shelf for book storage. Both types of desks go through Daltons' three production departments: fabrication, assembly, and packing/shipping, but required a different number of minutes in each department. For example, the regular desk needs 60 minutes of fabrication time, 45 minutes of assembly, and 15 minutes in packing & shipping. The deluxe model needs 120 minutes of fabrication time, 60 minutes in assembly, and 20 minutes in packing & shipping. Dalton has 850 hours of production time available in fabricating department, 450 hours available in its assembly department, and 200 hours available in its packaging and shipping department. Dalton reports unit profits of $6 and $8 for its regular and deluxe desks, respectively. What is the objective function? What is the fabrication constraint? What is the assembly constraint?What is the Shipping and Packing constraint?The Wellbuilt Company produces two types of wood chippers, economy and deluxe. The deluxe model requires 3 hours to assemble and 1/2 hour to paint, and the economy model requires 2 hours to assemble and 1 hour to paint. The maximum number of assembly hours available is 24 per day, and the maximum number of painting hours available is 8 per day. If the profit on the deluxe model is $94 per unit and the profit on the economy model is $70 per unit, how many units of each model will maximize profit? ___ deluxe units ___ Economy units
- ) John's Locomotive Works manufactures a model locomotive. It comes in two versions--a standard (X1), and a deluxe (X2). The standard version generates $250 per locomotive for the standard version, and $370 per locomotive for the deluxe version. One constraint on John's production is labor hours. He only has 34 hours per week for assembly. The standard version requires 280 minutes each, while the deluxe requires 390 minutes. John's milling machine is also a limitation. There are only 21 hours a week available for the milling machine. The standard unit requires 60 minutes, while the deluxe requires 120. Formulate as a linear programming problem, and solve using Excel Solver.A company manufactures two types of trucks. Eachtruck must go through the painting shop and the assembly shop. If the painting shop were com-pletely devoted to painting type 1 trucks, 650 per day could be painted, whereas if the painting shopwere completely devoted to painting type 2 trucks,550 per day could be painted. If the assembly shopwere completely devoted to assembling truck 1engines, 1400 per day could be assembled, whereasif the assembly shop were completely devoted toassembling truck 2 engines, 1000 per day could beassembled. It is possible, however, to paint bothtypes of trucks in the painting shop. Similarly, it ispossible to assemble both types in the assemblyshop. Each type 1 truck contributes $2500 to profit; each type 2 truck contributes $3000. Use Solver to maximize the company’s profit. (Hint: One ap-proach, but not the only approach, is to try a graphi-cal procedure first and then deduce the constraints from the graph.)You are working for Advance Technology, a company that produces three different devices for the military. The three devices that you produce are Main-bus Servo Modules, Secondary Trigger Activators, and Guidance Couplers. Advance Technology has two manufacturing facilities, the Croswell facility and the Grass Lake facility. Each day, the Croswell facility can produce 8 Main-bus Servo Modules, 4 Secondary Trigger Activators, and 4 Guidance Coupler at a cost of $1,800. Each day, the Grass Lake facility can produce 6 Main-bus Servo Modules, 12 Secondary Trigger Activators, and 2Guidance Couplers at a cost of $1,600. An order from the U.S. Navy for 210 Main-bus Servo Modules, 150 Secondary Trigger Activators, and 90 Guidance Couplers is received. Your boss has assigned to you the task of determining the number of days that each facility should operate to meet the order placed for the three devices at a minimum cost to your company.
- A linear programming computer package is needed. Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company's needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows. Component Supplier 1 2 3 1 $13 $14 $15 2 $11 $12 $11 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows. Supplier 1 2 3 Capacity 500 900 700 If the Edwards production plan for the next period includes 900 units of component 1 and 700 units of component 2, what purchases do you recommend? That is, how many…A linear programming computer package is needed. Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company's needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows. Component Supplier 1 2 3 1 $11 $12 $13 2 $9 $10 $9 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows. Supplier 1 2 3 Capacity 700 1,100 900 (a) If the Edwards production plan for the next period includes 1,100 units of component 1 and 900 units of component 2, what purchases do you recommend? That is,…A linear programming computer package is needed. 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 5,500 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 Manufacturing Cost Purchase Cost Frame $39.00 $52.00 Support $12.50 $16.00 Strap $7.50 $8.50 Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows. Component Department Cutting Milling…