2. RFC Company manufactures two types of lamps: a special lamp and a regular lamp. Each special lamp requires 4 pounds of brass and each regular lamp requires 8 pounds of brass. During each production period, the company's brass supply is limited to 640 pounds. Each special lamp requires 6 hours of milling time in the machines and each regular lamp requires 2 hours of milling time in the machines. The company's machines are available only for 360 hours in each production period. Each special lamp requires 5 light bulbs that must be imported from Hongkong. The importation of these bulbs is limited to 200 units. The contribution to the profit of each special lamp is P400 and P360 on the regular lamp. How many units of the special lamp and the regular lamp should be produced per production period in order to maximize the profit?
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- Plainwell Polymers is going to producing the main dashboard structure for a new car design. The dashboard will be produced in three colors with expected daily demand as follows: Black: 365 units/day Grey: 110 units/day Tan: 210 units/day The injection-molding machine can produce a total of 1,090 parts per day running 24 hours per day. It costs Plainwell $1,040 to set up each color for producition and the daily holding cost for each part is $0.49. What is the length of the lowest cost cyclic schedule (ignoring setup time constraints) in days?The Delta company uses three raw materials to make cakes. Delta is trying to reduce warehousing costs and establishes three policies to that end: i) The annual number of orders for all products must be at least 20 per contractual terms with transportation providers. ii) The average inventory in units must be a maximum of 1800. iii) Because the raw material is perishable, there can never be more than 2000 units in inventory of raw material 1. Raw material 2 has a maximum allowed of 1200 units and the raw material 3 can store maximum 400 units. The following table shows the product information: Materia Demanda Costos por unidad Costo por prima (u/año) ordenar ($) 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…In a large microelectronics plant, the assembly cell for circuit boards has a demand for 300 units an hour. Two feeder cells supply partsA and B to the assembly cell (one A and one B for each board). Standard containers that look like divided trays are used. A container will hold 22 As or 13 Bs. It takes 13 minutes to fill up a container with As and 22 minutes to fill up a container with Bs. Transit time to the assembly cell is 5 minutes for both A and B. No safety factor is used. Kanbans to be circulated Between Process A and Assembly cell? Kanbans to be circulated Between Process B and Assembly cell?
- 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?In a large microelectronics plant, the assembly cell for circuit boards has a demand for 250 units an hour. Two feeder cells supply parts A and B to the assembly cell (one A and one B for each board). Standard containers that look like divided trays are used. A container will hold 24 As or 10 Bs. It takes 10 minutes to fill up a container with As and 24 minutes to fill up a container with Bs. Transit time to the assembly cell is 5 minutes for both A and B. No safety factor is used. Set up a kanban control system for the assembly process.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…Jays Office Supplies sells Printers, which it orders from Brands mart Inc in . Because of shipping and handling costs, each order must be for 5 printers. Because of the time it takes to receive an order, the company places an order every time the present stock drops to 5 Printers. It costs $50 to place an order. It costs the company $500 in lost sales when a customer asks for a Printer and the warehouse is out of stock. It costs $100 to keep each Printer stored in the warehouse. If a customer cannot purchase a Printer when it is requested, the customer will not wait until one comes in but will go to a competitor. The following probability distribution for demand for Printer has been determined: Questions 1.Simulate CWD 's ordering and sales policy for 20 weeks 2. Compute the average cost of the policy PLEASE NOTE I SENT THIS IN ALREADY BUT I REALIZED I LEFT OUT SOME VITAL INFORMATION AND AGAIN THIS IS NOT FROM ANOTHER SITE.A brewery produces regular beer and a lower-carbohydrate "light" beer. Steady customers of the brewery buy 12 units of regular beer and 18 units of light beer monthly. While setting up the brewery to produce the beers, the management decides to produce extra beer, beyond that needed to satisfy customers. The cost per unit of regular beer is $32,000 and the cost per unit of light beer is $60,000. Every unit of reqular beer brings in $100,000 in revenue, while every unit of light beer brings in $300,000 in revenue. The brewery needs at least $9,000,000 in revenue, and has determined that the total demand will be at least 50 units of beer. Complete parts (a) and (b). (a) How much of each type of beer should be made so as to minimize total production costs? 30 units of regular beer and 20 units of light beer should be made, for a minimum total cost of $ 2160000 (Type integers or decimals.) (b) Suppose the minimum revenue is increased to $9,400,000. Use shadow costs to calculate the total…
- Bectol, Inc. is building a dam. A total of 10 million cuft of dirt is needed to construct the dam. A bulldozer is usedto collect dirt for the dam. Then the dirt is moved via dumpersto the dam site. Only one bulldozer is available, and it rentsfor $100 per hour. Bectol can rent, at $40 per hour, as manydumpers as desired. Each dumper can hold 1,000 cu ft ofdirt. It takes an average of 12 minutes for the bulldozer toload a dumper with dirt, and each dumper an average of fiveminutes to deliver the dirt to the dam and return to the bulldozer. Making appropriate assumptions about exponen-tiality, determine how Bectol can minimize the total expected cost of moving the dirt needed to build the dam.A manufacturing cell makes three models of a product – AKC1011, BC0001, and AC0102. The daily demand for the three products are as follows: 200 of AKC1011, 500 BC0001, and 300 of AC0102. Develop a balanced mixed-model sequence that should be repeated throughout the day in order to meet demand.A manufacturer has a production facility that requires 10,237 units of component JY21 per year. Following a long-term contract, the manufacturer purchases component JY21 from a supplier with a lead time of 6 days. The unit purchase cost is $31.4 per unit. The cost to place and process an order from the supplier is $168 per order. The unit inventory carrying cost per year is 12.2 percent of the unit purchase cost. The manufacturer operates 250 days a year. Assume EOQ model is appropriate. If the manufacturer uses a constant order quantity of 1,053 units per order, what is the annual holding cost? Use at least 4 decimal places.