A photocopy machine company produces three types of laser printers—the Print Jet, the Print Desk, and the Print Pro-the sale of which earn profits of $60, $90, and $73, respectively. The Print Jet requires 2.9 hours of assembly time and 1.4 hours of testing time. The Print Desk requires 3.7 hours of assem-
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- A company manufactures plastic bottles, buckets, and cups. The profit units are $10 for a plastic bottle, $25 for a bucket,and 58 for a bag of cups. The machine that makes the goods has a capacity of 400 hours each month. The bottle takestwo hours to make, the bucket three hours, and the cup one hour. The company has a total of 890 units of plastic. Plasticbottles require three units, buckets five units, and cups one unit. In addition, there are 200 kg of a novel chemicalcomponent. This unique chemical component is employed in plastic bottles (2 kilogram), buckets (4 kg), and cups (0.5kg) . There is an order to produce only 50 bags of plastic cup. The company wants to find the optimal plan to maximizeprofit. Use the Simplex method to solve this problem.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?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.
- 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.)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 unitsYou 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.
- Sidneyville manufactures household and commercial furnishings. The Office Division produces two desks, rolltop and regular. Sidneyville constructs the desks in its plant outside Medford, Oregon, from a selection of woods. The woods are cut to a uniform thickness of 1 inch. For this reason, one measures the wood in units of square feet. One rolltop desk requires 10 square feet of pine, 4 square feet of cedar, and 15 square feet of maple. One regular desk requires 20 square feet of pine, 16 square feet of cedar, and 10 square feet of maple. The desks yield respectively $115 and $90 profit per sale. At the current time the firm has available 200 square feet of pine, 128 square feet of cedar, and 220 square feet of maple. The firm has backlogged orders for both desks and would like to produce the number of rolltop and regular desks that would maximize profit. How many of each should it produce?Angela and Bob Ray keep a large garden in which they grow cabbage, tomatoes, and onions to make two kinds of relishchow-chow and tomato. The chow-chow is made primarily of cabbage, whereas the tomato relish has more tomatoes than chow-chow. Both relishes include onions, and negligible amounts of bell peppers and spices. A jar of chow-chow contains 8 ounces of cabbage, 3 ounces of tomatoes, and 3 ounces of onions, whereas a jar of tomato relish contains 6 ounces of tomatoes, 6 ounces of cabbage, and 2 ounces of onions. The Rays grow 120 pounds of cabbage, 90 pounds of tomatoes, and 45 pounds of onions each summer. The Rays can produce no more than 24 dozen jars of relish. They make $2.25 in profit from a jar of chow-chow and $1.95 in profit from a jar of tomato relish. The Rays want to know how many jars of each kind of relish to produce to generate the most profit. the Rays have checked their sales records for the past five years and have found that they sell at least 50% more…Angela and Bob Ray keep a large garden in which they grow cabbage, tomatoes, and onions to make two kinds of relish—chow-chow and tomato. The chow-chow is made primarily of cabbage, whereas the tomato relish has more tomatoes than does the chow-chow. Both relishes include onions, and negligible amounts of bell peppers and spices. A jar of chow-chow contains 8 ounces of cabbage, 3 ounces of tomatoes, and 3 ounces of onions, whereas a jar of tomato relish contains 6 ounces of tomatoes, 6 ounces of cabbage, and 2 ounces of onions. The Rays grow 120 pounds of cabbage, 90 pounds of tomatoes, and 45 pounds of onions each summer. The Rays can produce no more than 24 dozen jars of relish. They make $2.25 in profit from a jar of chow-chow and $1.95 in profit from a jar of tomato relish. The Rays want to know how many jars of each kind of relish to produce to generate the most profit.a. Formulate a linear programming model for this problem. c. Solve this model using simplex solution method.
- Angela and Bob Ray keep a large garden in which they grow cabbage, tomatoes, and onions to make two kinds of relish—chow-chow and tomato. The chow-chow is made primarily of cabbage, whereas the tomato relish has more tomatoes than does the chow-chow. Both relishes include onions, and negligible amounts of bell peppers and spices. A jar of chow-chow contains 8 ounces of cabbage, 3 ounces of tomatoes, and 3 ounces of onions, whereas a jar of tomato relish contains 6 ounces of tomatoes, 6 ounces of cabbage, and 2 ounces of onions. The Rays grow 120 pounds of cabbage, 90 pounds of tomatoes, and 45 pounds of onions each summer. The Rays can produce no more than 24 dozen jars of relish. They make $2.25 in profit from a jar of chow-chow and $1.95 in profit from a jar of tomato relish. The Rays want to know how many jars of each kind of relish to produce to generate the most profit.a. Formulate a linear programming model for this problem.b. Solve this model graphically.A company produces three different products; x,y, and z. For the production of 1 unit of product x, 1 unit of A and 1 unit of B are used as input. 1 unit of A and 2 units of B are used to produce 1 unit of product y. To produce 1 unit of product z, only 1 unit of A is used. The company holds 40 units of A and 20 units of B periodically in total. By the way, the company can not produce product y more than the twice of product z. On the other hand, the sale price of 1 unit of product x is 10 TL, product y is 15 TL and product z is 12 TL. Furthermore, the cost of 1 unit of product x is 8 TL, product y is 9 TL and product z is 7 TL. According to above information, what should be the company’s optimal product mix to maximize its profit? Construct the problem as a Linear programming model. Solve the above problem by using Simplex Method.A local bakery produces two popular items weekly: chocolate cakes and apple pies. The profit for a chocolate cake is $30, and an apple pie is $20. Each product requires two types of labor: baking and decorating. The chocolate cake needs 2 hours of decorating and 1 hour of baking, while an apple pie takes 1 hour for baking and 1 hour for decorating. The bakery has 1000 hours weekly for decorating and 800 hours for baking. Due to market demand constraints, the bakery should not produce more than 400 chocolate cakes per week. Hence, the bakery needs to know the optimal number of chocolate cakes and apple pies to maximize its total profit. a.) Draw the problem´s feasible region b.) What is the optimum number of chocolate cakes, apple pies, and profit? c.) what are the active and nonactive constraints?