Part A is processed on a MILLING machine; Part B is processed on a LATHE machine. Two parts (A and B) are then assembled on an ASSEMBLY machine. Standard times, scrap rates, efficiency, and availability of each machine and the assembly are given in the table below. Determine the number of milling (M), the lathe (L) and the assembly (A) machines needed to produce 100 good parts from this production system during and 8-hour (480 minutes) shift. (Note: Round up the number of parts processed on each station and then round up the number of machines needed)

Part A is processed on a MILLING machine; Part B is processed on a LATHE machine. Two parts (A and B) are then assembled on an ASSEMBLY machine. Standard times, scrap rates, efficiency, and availability of each machine and the assembly are given in the table below. Determine the number of milling (M), the lathe (L) and the assembly (A) machines needed to produce 100 good parts from this production system during and 8-hour (480 minutes) shift. (Note: Round up the number of parts processed on each station and then round up the number of machines needed)

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 111P

See similar textbooks

Similar questions

A company produces two products: A and B. Prod-uct A sells for $11 per unit and product B sells for $23 per unit. Producing a unit of product A requires two hours on assembly line 1 and one unit of raw ma-terial. Producing a unit of product B requires two units of raw material, one unit of A, and two hours on as-sembly line 2. On line 1, 1300 hours of time are avail-able, and 500 hours are available on line 2. A unit of raw material can be bought (for $5 a unit) or produced(at no cost) by using two hours of time on line 1.a. Determine how to maximize profit.b. The company will stop buying raw material whenthe price of raw material exceeds what value? (UseSolverTable.)
Terry, Inc., makes gasoline storage tanks. All production is done under contract. The company makes three basic models, but each model must be adapted to customer specifications for the location of outlets, insulation, and paint. It takes from three to six months to complete a tank. How should Terry account for the income for the business?
Exer Tread produces two types of exercise treadmills: regular and deluxe. The exercise craze is such that Exer Tread could use all its available machine hours to produce either model. The two models are processed through the same production departments. Data for both models are as follows: 1(Click the icon to view the data.) Read the requirements2. Requirement 1. What is the constraint? Exer Tread's constraint is machine hours . Requirement 2. Which model should Exer Tread produce? (Hint: Use the allocation of fixed manufacturing overhead to determine the proportion of machine hours used by each product.) Exer Tread should produce the product with the highest contribution margin per unit of the constraint . Now prepare the product mix analysis by starting with the contribution margin per unit. Deluxe Regular treadmill treadmill Sale price per unit…
Although the problems say solve graphically, please solve all problems using the QM for Windows software or solve manually. B.5 The Attaran Corporation manufactures two electrical products: portable air conditioners and portable heaters. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling Each heater must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are zvailable and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each heater assembled may be sold for a $15 profit. Formulate and solve this LP production-mix situation, and find the best combination of air conditioners and heaters that yields the highest profit.
The Crandon Manufacturing Company produces two principal product lines. One is a portable circular saw, and the other is a precision table saw. Two basic operations are crucial to the output of these saws: fabrication and assembly. The maximum fabrication capacity is 4000 hours per month; each circular saw requires 2 hours, and each table saw requires 1 hour. The maximum assembly capacity is 5000 hours per month; each circular saw requires 1 hour, and each table saw requires 2 hours. The marketing department estimates that the maximum market demand next year is 3500 saws per month for both products. The average contribution to profits and overhead is $900 for each circular saw and $600 for each table saw. Management wants to determine the best product mix for the next year so as to maximize contribution to profits and overhead. Also, it is interested in the payoff of expanding capacity or increasing market share.
Component D consists of 4 units of A, 1 unit of B, and 2 units of C. The table and figure indicate which facilities can produce which product (component or assembly). There is demand for 500 units of assembly D. The transportation costs between facilities 1 - 4 and facility 5 are identical. Total capacity to produce Band/or C at facility 3 is 800. To minimize costs , how much of C will be produced at facility 4? Only variable production costs need to be considered. Facility Variable production costs (€/unit} 1 10 (A) 2 12 (A); 14 ( B) 3 10 (B); 10 (C) 4 12 (C)
FRUIT COMPUTER COMPANY Fruit Computer Company manufactures memory chips in batches of ten chips. From past experience, Fruit knows that 80% of all batches contain 10% (1 out of 10) defective chips, and 20% of all batches contain 50% (5 out of 10) defective chips. If a good (that is, 10% defective) batch of chips is sent to the next stage of production, processing costs of $4000 are incurred, and if a bad batch (50% defective) is sent on to the next stage of production, processing costs of $16000 are incurred. Fruit also has the alternative of reworking a batch at a cost of $4000. A reworked batch is sure to be a good batch. Alternatively, for a cost of $400, Fruit can test one chip from each batch in an attempt to determine whether the batch is defective. QUESTIONS 1.Determine a strategy so Fruit can minimize the expected total cost per batch. 2.Compute the EVSI and EVPI.
Tuff-Rider, Inc., manufactures touring bikes and mountain bikes in a variety of frame sizes, colors, and component combinations. Identical bicycles are produced in lots of 100. The projected demand, lot size, and time standards are shown in the following table: Item Touring Mountain Demand forecast Lot size Standard processing time Standard setup time 5,000 units/year 100 units .25 hour/unit 2 hours/lot 10,000 units/year 100 units .50 hour/unit 3 hours/lot The shop currently works 8 hours a day, 5 days a week, 50 weeks a year. It operates five workstations, each producing one bicycle in the time shown in the table. The shop maintains a 15 percent capacity cushion. How many workstations will be required next year to meet expected demand without using overtime and without decreasing the firm’s current capacity cushion?
Prevost Chemicals manufactures an industrial solvent at its only processing plant. A liquid chemical and labor are the two primary inputs. All other resources are included in manufacturing overhead. The plant never has any work-in-process or finished goods inventories. Information from the previous four periods of production follows: Period 1 Period 2 Period 3 Period 4 Chemical input (gallons) 125,000 129,280 128,000 120,000 Labor input (hours) 12,500 11,200 15,000 10,100 Solvent sales (gallons) 110,000 113,120 120,000 103,020 Average price of chemical per gallon $ 2.00 $ 2.10 $ 1.95 $ 2.25 Average wage rate per hour 28.00 26.00 31.00 34.00 Average sales price per gallon 10.26 10.00 9.80 10.60 Manufacturing overhead (total) 236,000 245,312 245,400 243,080 Required: a. Compute the partial productivity measures for chemical for the four periods. b. Compute the partial productivity measures for labor for the four periods.
Prevost Chemicals manufactures an industrial solvent at its only processing plant. A liquid chemical and labor are the two primary inputs. All other resources are included in manufacturing overhead. The plant never has any work-in-process or finished goods inventories. Information from the previous four periods of production follows: Period 1 Period 2 Period 3 Period 4 Chemical input (gallons) 125,000 129,280 128,000 120,000 Labor input (hours) 12,500 11,200 15,000 10,100 Solvent sales (gallons) 110,000 113,120 120,000 103,020 Average price of chemical per gallon $ 2.00 $ 2.10 $ 1.95 $ 2.25 Average wage rate per hour 28.00 26.00 31.00 34.00 Average sales price per gallon 10.26 10.00 9.80 10.60 Manufacturing overhead (total) 236,000 245,312 245,400 243,080 Required: c. Compute the total factor productivity for the four periods.
Valencia Products makes automobile radar detectors and assembles two models: LaserStop and SpeedBuster. The firm can sell all it produces. Both models use the same electronic components. Two of these can be obtained only from a single supplier. For the next month, the supply of these is limited to 4,000 of component A and 3,500 of component B. The number of each component required for each product and the profit per unit are in the table below. This question is interested in maximizing the profit). a) Identify the decision variables, objective function, and constraints in simple verbal statements. b) Mathematically formulate a linear optimization model. Components Required/Unit A B Profit/Unit LaserStop 18 6 $124 SpeedBuster 12 8 $136 Solve this question in Excel by using SOLVER. Please clearly explain what is the optimal solution? What is the resulting output of the objective function at the optimal solution? P.S. please solve in Excel.
The Goodparts Company produces a component that is subsequently used in the aerospace industry. The component consists of three parts (A, B, and C) that are purchased from outside and cost 35, 30, and 10 cents per piece, respectively. Parts A and B are assembled first on assembly line 1, which produces 185 components per hour. Part C undergoes a drilling operation before being finally assembled with the output from assembly line 1. There are, in total, six drilling machines, but at present only three of them are operational. Each drilling machine drills part C at a rate of 80 parts per hour. In the final assembly, the output from assembly line 1 is assembled with the drilled part C. The final assembly line produces at a rate of 205 components per hour. At present, components are produced eight hours a day and five days a week. Management believes that if the need arises, it can add a second shift of eight hours for the assembly lines. The cost of assembly labor is 30 cents per part for…