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Each bookcase yields a $12 profit. Watson's firm is small and its resources limited. During any given production period (of 1week),8 gallons of varnish and 14 lengths of high-quality redwood are available. Each coffee table requires approximately 1gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
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- . A commercial orchard grows, picks, and packs apples and pears. A peck (quarter bushel) of apples takes 4 minutes to pick and 5 minutes to pack; a peck of pears takes 5 minutes to pick and 4 minutes to pack. Only one picker and one packer are available. How many pecks each of apples and pears should be picked and packet every hour (60 minutes) if the profit is $3/peck for apples and $2/peck for pears? Solve graphically as a linear program and confirm analytically.Dark beer is purchased by the case for $18.90. There are 24 bottles in each case, and each bottle contains 12 fluid ounces. You are making brine that requires 2 ½ quarts of dark beer. How much will the beer cost for the brine?List the system of inequalities which describe B in the graph below.ECON1003 Mathematics for Social Sciences Unit 3_Version 1 Page 33 6. Anya’s Jeans has production process organized in threedistinct stages: cutting; sewing and finishing. She produces threetypes of jeans, namely peddle-pushers, hipsters and low cuts. Thenumber of minutes each type requires in each production processin shown below.Type Cutting Sewing FinishingPeddle-Pusher 4 6 2Hipster 6 7 4Low Rider 9 3 6On average, there are 6400 minutes of cutting time, 3500 minutes ofsewing time and 2400 minutes of finishing time each day. Given thatthe company makes $10 profit on each peddle-pusher $ 50 on eachhipster and $60 on each low cut and that the company sells all thejeans made. List the system of inequalities for the cutting, sewingand finishing constraints.
- 2.28 A foundry produces castings to order. An order for 20 special castings has been re- ceived. Since the casting process is highly variable, not all castings produced are good. The cost of producing each casting is $550; the additional cost of finishing a good casting is $125. If a casting is not good, it is recycled at a value of $75; excess good castings are not finished but are recycled at a value of $75. The customer has agreed to accept 15, 16, 17, 18, 19, or 20 castings at a price of $1250 each. If fewer than 15 good castings are produced, none will be purchased by the customer. Prob- ability distributions for the number of good castings produced in a batch of varying sizes are given below. How many castings should be scheduled in order to maximize expected profit? #Good Castings 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 79 2 PRODUCT, PROCESS, AND SCHEDULE DESIGN Number of Castings Scheduled 15 16 17 0.05 0.00 0.00 0.00 0.00 0.00 0.05 0.05 0.00…Mack’s guitar fabrication shop produces low cost, highly durable guitars for beginners. Typically, out of the 100 guitars that begin production each month, only 80 percent are considered good enough to sell. The other 20 percent are scrapped due to quality problems that are identified after they have completed the production process. Each guitar sells for $300. Because some of the production process is automated, each guitar only requires 10 labor hours. Labor is paid at $10/hour, materials cost is $40/guitar, and overhead is $2,000. a) Calculate the labor and multifactor productivities. b) After some study, the operations manager recommends 3 options to improve the company’s multifactor productivity: (1) increase the sales price by 10 percent, (2) improve quality so that only 10 percent are defective, or (3) reduce labor, material, and overhead costs by 10 percent. Which option has the greatest impact on the multifactor productivity measure?XYZ Corporation manufactures two products, Simple and Complex. The following annual information was gathered: Simple Complex Selling price per unit P47.00 P26.00 Variable cost per unit 42.00 22.00 Total annual fixed costs are P18,000. Assume XYZ Corporation can produce and sell any mix of Simple or Complex at full capacity. It takes one hour to make one unit of Complex. However, Simple takes 50% longer to manufacture when compared to Complex. Only 120,000 hours of plant capacity are available. How many units of Simple and Complex should XYZ Corporation produce and sell in a year to maximize profits?
- You are asked to help your boss deciding who is considering whether to make or buy a part fora top most demanding product of the company.Your company can make the component for $40 per unit or buy it for $50 per unit from vendor.If the Company decides to make the component, it will require 4 hours of machine time tomake each part. The company has 2,000 hours of machine time available per month. Shouldthe company make or buy the component? How many max parts company can make?________________________________________________________________The Delta company uses three raw materials to make cakes. Delta is trying to reduce warehousing costs and establishes three policies to that end: i) The annual number of orders for all products must be at least 20 per contractual terms with transportation providers. ii) The average inventory in units must be a maximum of 1800. iii) Because the raw material is perishable, there can never be more than 2000 units in inventory of raw material 1. Raw material 2 has a maximum allowed of 1200 units and the raw material 3 can store maximum 400 units. The following table shows the product information: Materia Demanda Costos por unidad Costo por prima (u/año) ordenar ($) 2200 2 300 2 500 4 650 3 3000 10 100 Consider an interest rate of 10% per year. A) Formulate the problem as a mathematical programming model that minimizes the total annual cost. b) Represent the problem in a single equation including the constraints in terms of lambda c) Find the optimized batch sizes for the company's raw…2. A machine part can be exhausted either from aluminum or steel. There is an order of 8,000 units.Steel costs 3.80Php/kg, while aluminum cost 8.70Php/kg. If steel is used, the steel per unit weighs110g and 30g for aluminum. In production, steel is 50 units/hr and 80units/hr with an aid of a toolcosting 640Php, which will be useless after the 8,000 units are finished. The cost of the machineoperator is 10.80Php/hr. if all other costs are identical, which material is more economical?a. Aluminum, by 1,264Php cost difference.b. Aluminum, by 1,653Php cost differencec. Steel, by 640Php cost difference.d. Steel, by 1,088Php cost difference.e. None of the above
- Please do not give solution in image format thanku In 2018, the government of Ghana launched operation one district one factory (IDIE). Based on IDIF, Ekumfi Pineapple Factory Co. Ltd (EPF) was launched. In 2019 the management of ERF started production with 100 workers per shift, each of the three shifts working 8 hours per day. Every working day the payroll cost was GHIC 20,000 and overhead expenses amounted to GHC 5000 and material cost GHC 4000. At the end of the first year, the company produced 1,000,000 boxes of pineapple juice. During the second year, EPF acquired a loan from Exim Bank to purchase a new plant. After the introduction of the new plant, the management reduced the size of its workers per shift to 80, each working 8 hours per day, with the payroll cost reducing to GHC 18,000 and overhead expenses also reducing to GHC 4000 and material cost rising to GHC 6000. Production rose to 1,200,000 boxes. Regard yourself as the Operations Manager of EPF: a) What are the…d) A company can produce three products A, B and C. the products yield a contribution of Kshs.8, 5 and 10 respectively. The products use a machine which has 400 hours capacity. Each unit of the product uses 2, 3 and 1 hour respectively of the machines capacity. There are only 150 units available in the period of a special component which is used singly in product A and C. Only 200kgs of a special alloy is available in the period. The usage of special alloy is 2kgs per unit and 4kgs per unit respectively. There is an agreement with a trade association to produce no more than 50 units of product B in the period. Advise the company on the production plan that will maximize contribution.CPG Bagels starts the day with a large production run of bagels. Throughout the morning additional bagels are produced as needed. The last bake is completed at 3 pm, and the store closes at 8 pm. It costs approximately $0.56 in materials and labor to make a bagel. The price of a fresh bagel is $2.29. Bagels not sold by the end of the previous day are sold the next day as "day- old" bagels for $0.15 each. CPG Bagels uses the Newsvendor model to management the inventory of the bagels. The critical ratio %. Report the answer without the percentage sign and keep one decimal in your answer. For example, if your answer is 0.9232 (92.32%), report 92.3 in your answer.