Find decision variables, objective function, constraints and non-negativity constraints An auto company manufactures cars and trucks. Each vehicle must be processed in the paint shop and body assembly shop. If the paint shop were only painting trucks, 40 per day could be painted. If the paint shop were only painting cars, 60 per day could be painted. If the body shop were only producing cars, it could process 50 per day. If the body shop were only producing trucks, it could process 50 per day. Each truck contributes $300 to profit and each car contributes $200 to profit. In addition, the auto company can produce at most 30 trucks and 20 cars. The company wants to determine the daily production schedule that will maximize the company’s profit. Formulate the LP model for the problem.

Find decision variables, objective function, constraints and non-negativity constraints An auto company manufactures cars and trucks. Each vehicle must be processed in the paint shop and body assembly shop. If the paint shop were only painting trucks, 40 per day could be painted. If the paint shop were only painting cars, 60 per day could be painted. If the body shop were only producing cars, it could process 50 per day. If the body shop were only producing trucks, it could process 50 per day. Each truck contributes $300 to profit and each car contributes $200 to profit. In addition, the auto company can produce at most 30 trucks and 20 cars. The company wants to determine the daily production schedule that will maximize the company’s profit. Formulate the LP model for the problem.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 69P: The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon...

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The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.
For a certain civil engineering system, it is sought to maximize the benefits, which is given by the expression: Z=3x+5y. The decision variables are x (the amount of resource type 1 to be used) and y (the amount of resource type 2 to be used). • The amount of resource type 1 should be at least 3 units. • The amount of resource type 2 should be at least 3 units. The difference between the amount of ● resource type 2 and the amount resource type 1 should not exceed 6. • The total amount of resource types 1 and 2 should not exceed 12 units. a. Identify the obiective function for this problem. b. Identify and write the constraints. c. Provide a sketch graph for the constraint set. d. Clearly show the feasible region. e. Label all extreme points (or vertices) of the feasible region and indicate their coordinates. f. Solve the optimization problem.
A recurring maintenance job in a factory is being done by a three-man crew. Due to the nature of the job and space limitations, it was observed that two of the men were idle 37% of the time; one of the men was also idle an additional of the time, and at any given time only one man was required. The men were each paid P24.00 per hour. Each time the job was performed a set of tools and equipment with a value equivalent to P36.00 per hour was used. If the three-men crew could complete the work in 5 hours, which crew size would be the most economical
A company makes two products (A and B). Each product requires time on two machines 1 and 2. the specifications for each product are as follows Product A Product B Processing time on machine 1 (hrs/unit) Processing time on machine 2 (hrs/unit) Material and labor cost (Sh./ unit) Selling price (Sh./ unit) Maximum possible sale (units) 2 1 2 14 15 16 18 130 150 The amount of time available on machine 1 is 360 hrs and on machine 2 is 260 hrs. Using simplex method determine the number of product A and B, which should be sold in order to maximize total contribution for the company.
4. The Spencer Optics Company produces an inexpensive line of sunglasses. The manufacturing process consists of assembling two plastic lenses (produced by the firm's plastic molding depart- ment) into a finished frame (purchased from an outside supplier). The company is interested in using material requirements planning to schedule its operations and has asked you to prepare an example to illustrate the technique. The firm's sales manager has prepared a 10-week sales forecast for one of the more popular sunglasses (the Classic model) for your example. The forecast is 100 units per week. Spencer has customer orders of 110 units, 80 units, 50 units, and 20 units in weeks 1, 2, 3, and 4, respectively. The sunglasses are assembled in batches of 300 units. Presently, three such batches are sched- uled: one in week 2, one in week 5, and one in week 8. Complete the following time-phased record: Week hand 1 2 3 4 5 6 7 8 9 10 Classic Model On MPS Record Forecast Orders Projected available…
To be effective, an organization must have clearly defined sets of goals and objectives. True lr false
A company plans to produce 25,000 units in a 3-month period. The months have 22, 21, and 20 working days, respectively. What should the average daily production be?
Create a Crow’s Foot notation ERD to support the following business operations: Create a Crowsfoot notation ERD to support the following business operations: - A friend of yours has opened Marshfield Electronics and Repairs (MER) to repair smartphones, laptops, tablets, and MP3 players. She wants you to create a database to help her run her business. When a customer brings a device to MER for repair, data must be recorded about the customer, the device, and the repair (also referred to as repair request). Completing each repair request can involve multiple services (e.g. glass replacement, battery replacement, cleaning. Some services require parts. The customer’s name, address, and a contact phone number must be recorded. For the device to be repaired, the type of device, model, and serial number are recorded (or verified if the device is already in the system). Each repair request is given a reference number, which is recorded in the system along with the date of the request, and a…
Design capacity is the ability of the company to produce the quantity of goods and services within a particular period of time when the company have best condition to produce and when the company have unlimited resources. These resource's includes- Men, Machinery, Material etc. It shows the maximum capacity of the company to produce. Effective capacity refers to the ability of the company to produce maximum quantity within a particular period of time to achieve in current production condition and current resources. It shows the real outcome capacity of the firm when the company produce within their own current condition of their production. Question Why is the capacity design important?
1. Power Notebooks, Inc. plans to manufacture a new line of notebook computers. Management is trying to decide whether to purchase the LCD screens for the computers from an outside supplier or to manufacture the screens in-house. The screens cost $100 each from the outside supplier. To set up the assembly process required to produce the screens in-house would cost $100,000. The company could then produce each screen for $75. The number of notebooks that eventually will be produced (Q) is unknown at this point. a. Set up a spreadsheet that will display the total cost of both options for any value of Q. Use trial-and-error with the spreadsheet to determine the range of production volumes for which each alternative is best. b. Use a graphical procedure to determine the break-even point for Q (i.e., the quantity at which both options yield the same cost). 2. Back Savers is a company that produces backpacks primarily for students. They are considering offering some combination of two…
Design capacity is the ability of the company to produce the quantity of goods and services within a particular period of time when the company have best condition to produce and when the company have unlimited resources. These resource's includes- Men, Machinery, Material etc. It shows the maximum capacity of the company to produce. Effective capacity refers to the ability of the company to produce maximum quantity within a particular period of time to achieve in current production condition and current resources. It shows the real outcome capacity of the firm when the company produce within their own current condition of their production. In design capacity it is assume that the company will produce in best and ideal condition to produce goods and services while in Effective capacity it is assume that company will produce in current operating conditions. In design capacity it is assume that the company have unlimited resource's. It means these resource's include:- Men,…
Satomi w eks in a research facility that provides statistical results for the bioengineering firm TechCure. She is one of four interns expected to go through hendreds of samples per day. At her first week on the job, ber supervisor informs her that all blood sammples are to be completely anonymous. No testing can be done if personal information is revealed-meaning, the samples must be properly disposed of if opened, or veturned to the plysicians if unopened to be re- Aonymized. For the first five weeks, most of the new interns follow procedwes to check that samples were anonymized before testing occurred. However, one of the interns, Max, failed to verify whether the samples were anonymized. Halfway through the testing, Satomi discovers the non-anonymized samples. She considers whether they should tell their supervisor, but the other interns ask ber not to speak up so that they won't pet in trouble. of the interas argues that as long as they remove the information from the…