Concept explainers
a)
To explain: The data that is required as inputs for the model.
Linear programming:
It is a mathematical modeling procedure were a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
b)
To explain: The objective functions for this model.
Linear programming:
It is a mathematical modeling procedure were a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
c)
To explain: The constraints required for the model.
Linear programming:
It is a mathematical modeling procedure were a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
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Chapter 4 Solutions
Practical Management Science
- Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?arrow_forward(d) A company has three factories. Each factory produces three different products (A, B and C). Factory 1 has a daily production capacity production of 8 units of A, 4 units of B and 8 units of C. Factory 2 has a daily production capacity of 6 units of A, 6 units of B and 3 units of C. Factory 3 has a production capacity of 12 units of A, 4 units of B and 8 units of C. The total demand for product A is 300 units, for product B is 172 units and for product C is 250 units. The daily operating cost for Factory 1 is $55 for Factory 2 is $60 and for Factory 3 How many days should each factory be operated in order to fill the total demand and the keep the operating cost at a minimum? (i) (ii) (iii) $50. Show a model that represents the company's problem. Write down the dual maximization problem. Write down the initial simplex tableau.arrow_forward(c) A company manufactures two products: X and Y. Product X costs $8 per unit and contains 2 units of raw material 1, 6 units of raw material 2 and 4 units of raw material 3. Product Y costs $10 per unit and contains 2 units of raw material 1, 2 units of raw material 2 and 12 units of raw material 3. The company has 80 units of raw material 1, 120 units of raw material 2 and 240 units of raw material 3 available. In addition, the product Y should be at least 15 units less than product X. How many units of each product should the company produce to minimize the cost of production? (i) (ii) Derive the system of equations. Use the extreme point method to solve the system. Ensure that you explain each step in the computation.arrow_forward
- (b) A company produces 3 products A, B and C processed on 3 machines P, Q, R before completion. Machine P can process 25 units of A or 50 unit of B or 75 units of C per hour. Machine Q can process 50 units of any of the products per hour. Machine R can process 50 units of A or 25 unit of B or 100 units of C per hour. The processing hours available on machines P, Q and R are 12, 12 and 13 respectively. Use matrix method, find (i) How many units of each of the three products can be produced per day (ii) The production cost per unit, if cost per hour of operating machines A,B and C are N$500, N$1,000 and N$1,500 respectively. (iii) The total cost of production.arrow_forwardB & Carrow_forwardThe owner of a machine shop is planning to expand by purchasing some new machines-presses and lathes. The owner has estimated that each press purchased will increase profit by P5000 per day and each lathe will increase profit by P7500 daily. The number of machines the owner can purchase is limited by the cost of the machines and the available floor space in the shop. The machine purchase prices and space requirements are as follows: Required Floor Space (m2). Purchase Price Press 1.4 P400,000 Lathe 2.8 200,000 The owner has a budget of P2,200,000 for purchasing machines and 22 square meters of available floor space.arrow_forward
- Sapphire Farm is a business that trains and boards horses and educates young riders about horse care, nutrition, and riding. The farm provides both a learning and a fun environment for young equestrians and their families. It also hosts horse shows for beginning riders to help them build confidence in the show ring and to prepare them for local horse shows by running shows in accordance with the rules and regulations of the National Hunter Jumper Association. Feedback from the horseshow judges are provided to all riders so they can do better at their next meet. In addition, all warm-up and training areas are fenced and monitored by adults for the children's safety. If the farm unintentionally hired someone to teach riding who was unable to deal effectively with small children, then a _____ would occur. A. service divergence B. quality underperformance C. performance breakdown D. product variation E. customer aberrationarrow_forwardThank you so mucharrow_forwardAuthor: Leo A. Ruggle, Professor, Department of Accounting, Mankato State University Arnie Armstrong has been with Pierce Auto Parts Manufacturing Company for 23 years. Recently, he was appointed Director of Manufacturing Computer Services. In just six weeks in this new position, [he] has moved to reduce the amount of information provided to manufacturing department managers by 60 percent. He argues that excess data is distracting, unused, and expensive to provide. Willy McClean has been department manager for 12 years. During a coffee break with some of his department production supervisors, Willy is quite vocal about the change. “Who’s this guy Armstrong to tell us what data we need? He needs to be out here for a few weeks to find out what it’s like. Keep it quiet, but I’ve got a contact in Computer Services who’ll get me all the data analyses I want for just a $20 bill each month. It’s a good deal, and Armstrong will never know. How does he expect us to make good decisions about…arrow_forward
- Please solve this with proper explanationarrow_forwardThe Fly-Right Airplane Company builds small jet airplanes to sell to corporations for use by their executives. To meet the needs of these executives, the company's customers sometimes order a custom design of the airplanes being purchased. When this occurs, a substantial start-up cost is incurred to initiate the production of these airplanes. Fly-Right has recently received purchase requests from three customers with short deadlines. However, because the company's production facilities already are almost completely tied up filling previous orders, it will not be able to accept all three orders. Therefore, a decision now needs to be made on the number of airplanes the company will agree to produce (if any) for each of the three customers. The relevant data are given in the next table. The first row gives the start-up cost required to initiate the production of the airplanes for each customer. Once production is under way. the marginal net revenue (which is the purchase price minus the…arrow_forwardConsider the following short case as you respond to the question:Abruzzi's Italian Kitchen is a small family restaurant with an administrative staff of four people. Giuseppi Abruzzi is the chief executive officer; his wife Maria is the chief financial officer. Their son Antonio is responsible for all transactions dealing with kitchen supplies, including the raw materials for menu items; their son Carlo is responsible for all transactions dealing with dining room supplies, such as eating utensils. The restaurant's administrative practices have developed over the ten years of its existence with minimal reliance on information technology and formal procedures and a stronger emphasis on interpersonal relationships with a few reliable vendors. Once a month, Antonio places orders for kitchen supplies with one of four vendors based on price; the supplies are usually received within ten calendar days. On receipt of the supplies, Antonio pays the vendor with a company check. Carlo follows a…arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,