2. Four products are processed sequentially on three machines in an aircraft maintenance workshop. The following Table 1 gives the operational data of the problem. Machine 1 2 3 Unit selling price ($) Table 1: Operational data for the problem Cost per hr Product $ 1 2 3 7 75 10 5 4 Manufacturing time (hr) per unit Product Product Product 2 3 4 3 2 2 2 3 1 70 45 4 1 2 55 Capacity (hr) 500 380 450 (a) Formulate the problem as a Linear Programming (LP) problem (b) Determine the optimal product-mix in the production schedule and the optimal profit
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- A manufacturing firm closed down the production of a certain unprofitable product line.This necessitated the rational utilization of released excess production capacity.Management has been contemplating to devote this excess capacity to the manufacture of one or more of the three products A, B and C. The details about available excess machine capacity and machine requirements for the various products are given in I and II.I. Machine Type Available access Machine Time Milling Machine 250 hours / week Lathe 150 hours /week Ginder 50 hours /week II. Machine Type Machine hour requirements per unit of product A B C Milling Machine 8 2 3 Lathe 4 3 0 Ginder 2 0 1 It was assumed that the unit profit would be $20, $6 and$8 respectively, for products A, B and C. i. Formulate the L.P. problemii. Solve the problem by simplex methodThe Trim-Look Company makes several lines of skirts,dresses, and sport coats. Recently, a consultant suggested thatthe company reevaluate its South Islander line and allocateits resources to products that would maximize contributionto profits and to overhead. Each product requires the samepolyester fabric and must pass through the cutting and sewingdepartments. The following data were collected for the study: The cutting department has 100 hours of capacity, sewing has180 hours of capacity, and 60 yards of material are available.Each skirt contributes $5 to profits and overhead; each dress,$17; and each sport coat, $30.a. Specify the objective function and constraints for thisproblem.b. Use a computer package such as POM for Windows tosolve the problem.Sunseel Industries produces two types of raw materials, A and B, with a production cost of $4 and $8 per unit, respectively. The combined production of A and B must be at least 700 units per month. The factory is expected to produce at least 400 units of B and not more than 1200 units of A each month. The processing times for A and B are observed to be 5 hours and 4 hours, respectively. A total of 3000 production hours are available per month. Develop a linear program that Sunseel Industries can use to determine the number of units of each raw material to produce that will meet the demand and minimize the total cost.
- A manufacturing firm has four plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Factory (capacity) Customer 1 (125) Customer 2 (150) Customer 3 (175) Customer 4 (75) A (100) $ 15 $ 10 $ 20 $ 17 B (75) $ 20 $ 12 $ 19 $ 20 C (100) $ 22 $ 20 $ 25 $ 14 D (250) $ 21 $ 15 $ 28 $ 12 Note: This question requires Solver.Formulate the problem in Solver and find the optimal solution. What is the optimal quantity to ship from Factory B to Customer 3? Multiple Choice 25 units 50 units 75 units 100 units 125 unitsA machine shop manufactures two types of bolts. The bolts require time on each of the three groups of machines, but the time required on each group differs, as shown in the table below. Type I Type IIMachine 1 0.2 min 0.2 minMachine 2 0.6 min 0.2 minMachine 3 0.04 min. 0.08 min Production schedules are made up one day at a time. In a day, 300, 720, and 100 minutes are available, respectively, on these machines. Type I bolts sell for 15¢ and type II bolts for 20¢. (a) How many of each type of bolt should be manufactured per day to maximize revenue?(b) What is the maximum revenue?(c) Suppose the selling price of type I bolts began to increase. Beyond what amount would this price have to increase before a different number of each type of bolts should be produced to maximize revenue?1. Suppose the profit per table changed to $950. Will the optimal solution change, and what can be said about the effect on total profit? 2. Suppose the profit per table changed to $800. Will the optimal solution change, and what can be said about the effect on total profit? This would not change the optimal solution because the increase is within the allowable increase. 3. Suppose there are 300 less minutes available for Assembly. What can be said about the effect on total profit? 4. Suppose the company had an opportunity to acquire 500 minutes of Finishing capacity for a total cost of $2300. Should they do so? Explain. *Profit= Objective Coefficient
- Don't use chatgpt, I will 5 upvotes Alan wants to bake blueberry muffins and bran muffins for the school bake sale. For a tray of blueberry muffins, Alan uses 1/3 cup of oil and 2 eggs. For a tray of bran muffins, Alan uses 1/2 cup of oil and 1 egg. Alan has 4 cups of oil and 12 eggs on hand. He sells trays of blueberry muffins for $12 each and trays of bran muffins for $9 each. Alan wants to maximize the money raised at the bake sale. Let x represent the number of blueberry muffins and y represent the number of bran muffins Alan bakes.#1- Maxwell Manufacturing makes two models of felt tip marking pens. Requirements and available resources for each lot of pens are given in the following table: Fliptop Model Tiptop Model Available Plastic 3 4 36 Ink Assembly 5 4 40 Molding Time 5 2 30 The profit for either model is $1,000 per lot. a) What is the linear programming model for this problem? b) Using Microsoft Excel's Solver, find the optimal solution. How many Fliptop models and how many Tiptop models should be produced? What is the maximum profit? c) Will there be excess capacity in any resource? Use Excel's Solver and run a sensitivity report to answer the following questions. d) Over which range can the objective function coefficient for Fliptop Models change without affecting the original optimal solution? What is this range called? e) What is the shadow price (dual price) for the plastic constraint and how would you interpret it? f) What is the shadow price (dual price)…Although the problems say solve graphically, please solve all problems using the QM for Windows software or solve manually. B.6 The Christina Alvarez Company manufactures two lines of designer yard gates, called model A and model B. Every gate requires blending a certain amount of steel and zinc, the company has available a total of 25.000 Ib of steel and 6,000 lb of zinc. Each model A gate requires a mixture of 125 Ib of steel and 20 lb of zinc, and each yields a profit of 590. Each model B gate requires 100 1b of steel and 30 ib of zinc and can be sold for a profit of $70. Find by graphical IP the best production mix of yard gates.
- RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 ton of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced.RMC’s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material:Raw Material Amount Available for ProductionMaterial 1 20 tonsMaterial 2 5 tonsMaterial 3 21 tonsAssuming that RMC is interested in maximizing the total profit contribution, answer the following:i. Compute the value of the objective function…RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 ton of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced.RMC’s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material:Raw Material Amount Available for ProductionMaterial 1 20 tonsMaterial 2 5 tonsMaterial 3 21 tonsAssuming that RMC is interested in maximizing the total profit contribution, answer the following:a. What is the linear programming model for this…The Westerbeck Company manufactures several models of automatic washers and dryers. The projected requirements over the next year for their washers are shown in the table below: Month & Requirement January - 710 February - 1090 March - 880 April - 690 May - 1400 June - 1130 July - 1550 August - 1020 September - 530 October - 390 November - 980 December - 1210 Current inventory is 140 units. Current capacity is 1,030 units per month. The average salary of production workers is $1,150 per month. Material costs $140/unit. Each production worker accounts for 35 units per month. Overtime is paid at time and a half. Any increase or decrease in the production rate costs $40/unit for tooling, setup, and line changes. This does not apply, however, to overtime. Inventory-holding costs are $30 per unit per month. Lost sales are valued at $70 per unit. Compare the costs of level and chase demand production plans using the Agg Plan – Level and Agg Plan – Chase…