Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 3.8, Problem 24P
Summary Introduction
To determine: The change in the optimal production
Introduction: In linear programming, the unbounded solution would occur when the objective function is infinite. If no solution satisfied the constraints, then it is said to be an unfeasible solution.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
In a typical production scheduling model like Pigskin’s, if there are no production capacity constraints—the company can produce as much asit needs in any time period—but there are storage capacity constraints and demand must be met on time, is it possible that there will be no feasible solutions? Why or why not?
In the Great Threads model, we found an upper bound on production of any clothing type by calculating the amount that could be produced if all of the resources were devoted to this clothing type. a. What if you instead use a very large value such as 1,000,000 for this upper bound? Try it and see whether you get the same optimal solution. b. Explain why any such upper bound is required. Exactly what role does it play in the model?
A company needs to schedule the monthly production of a certain item for the next 4 months. The unit production cost is estimated to be $12 for the first 2 months and $14 for the last two months. The monthly demands are 750, 1000, 850 and 950 units. The company can increase the monthly production during the second and third months by utilizing overtime. The increase in production by this measure is limited to 400 units per month, and costs an extra $4 per unit. The regular production capacity is 1000 units/month. Excess production can be stored at a cost of $3 per unit per month, but a maximum of 50 units can be stored in any month. Assuming that the beginning and ending inventory levels are zero, formulate this problems as an LP model so that the total cost s minimized.
Chapter 3 Solutions
Practical Management Science
Ch. 3.6 - Prob. 1PCh. 3.6 - Prob. 2PCh. 3.6 - Prob. 3PCh. 3.6 - Prob. 4PCh. 3.6 - Prob. 5PCh. 3.6 - Prob. 6PCh. 3.6 - Prob. 7PCh. 3.6 - Prob. 8PCh. 3.6 - Prob. 9PCh. 3.7 - Prob. 10P
Ch. 3.7 - Prob. 11PCh. 3.7 - Prob. 12PCh. 3.7 - Prob. 13PCh. 3.7 - Prob. 14PCh. 3.7 - Prob. 15PCh. 3.7 - Prob. 16PCh. 3.7 - Prob. 17PCh. 3.8 - The Pigskin Company produces footballs. Pigskin...Ch. 3.8 - The Pigskin Company produces footballs. Pigskin...Ch. 3.8 - The Pigskin Company produces footballs. Pigskin...Ch. 3.8 - Prob. 21PCh. 3.8 - Prob. 22PCh. 3.8 - Prob. 23PCh. 3.8 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 28PCh. 3 - Prob. 29PCh. 3 - Prob. 30PCh. 3 - Prob. 31PCh. 3 - Prob. 32PCh. 3 - Prob. 33PCh. 3 - Prob. 34PCh. 3 - Prob. 35PCh. 3 - Prob. 36PCh. 3 - Prob. 37PCh. 3 - Prob. 38PCh. 3 - Prob. 39PCh. 3 - Prob. 40PCh. 3 - Prob. 41PCh. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Prob. 44PCh. 3 - Prob. 45PCh. 3 - Prob. 46PCh. 3 - Prob. 47PCh. 3 - Prob. 48PCh. 3 - Prob. 49PCh. 3 - Prob. 50PCh. 3 - Prob. 51PCh. 3 - Prob. 52PCh. 3 - Prob. 1C
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.Similar questions
- The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the decision variable cells and the objective cell.arrow_forwardThe Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)arrow_forwardThe Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?arrow_forward
- Based on Zangwill (1992). Murray Manufacturing runs a day shift and a night shift. Regardless of the number of units produced, the only production cost during a shift is a setup cost. It costs $8000 to run theday shift and $6000 to run the night shift. Demand for the next two days is as follows: day 1, 4000; night 1, 3000; day 2, 2000; night 2, 5000. It costs $1 per unit to hold a unit in inventory for a shift.a. Determine a production schedule that minimizes the sum of setup and inventory costs. All demand must be met on time. (Note: Not all shifts have to be run.)b. After listening to a seminar on the virtues of the Japanese theory of production, Murray has cut the setup cost of its day shift to $1000 per shift and the setup cost of its night shift to $3500 per shift. Nowdetermine a production schedule that minimizes the sum of setup and inventory costs. All demand must be met on time. Show that the decrease in setup costs has actually raised the average inventorylevel. Is this…arrow_forwardYou are the finance manager of the firm Sunderland Plastics Limited, which produces two products (X1 and X2) using two different machines (M1 and M2). Each unit of X1 requires 4 hours of processing time on M1 and 2 hours of processing time on M2. Each unit of X2 that gets produced requires a 1 hour processing time on M1 and 1.5-hour processing time on M2.The firm has an available processing time of 40 hours of M1 and 30 hours of M2 available this week. The firm also meets the non-negativity constraints. Your task is the following:The firms makes a net profit of 400 USD from 1 unit of product X1 and 100 USD from 1 unit of product X21) Formulate a linear programming problem in the standard form for Sunderland Plastics Limited.2) Solve the problem graphically and show what combination of the products X1 and X2 the firm should produce to maximise its profit while satisfying the constraints it is facing. How much profit will the firm make?arrow_forwardA company produces A, B, and C and can sell theseproducts in unlimited quantities at the following unit prices:A, $10; B, $56; C, $100. Producing a unit of A requires 1hour of labor; a unit of B, 2 hours of labor plus 2 units ofA; and a unit of C, 3 hours of labor plus 1 unit of B. AnyA that is used to produce B cannot be sold. Similarly, anyB that is used to produce C cannot be sold. A total of 40hours of labor are available. Formulate an LP to maximizethe company’s revenues.arrow_forward
- A company estimates the demand for its products for the next three periods as follows. The first period is 20 units, the second period is 10 units, and the third period is 15 units. The manufacturing costs for producing the product are as follows: period 1—$13; period 2— $14; period 3—$15. If the number of products in each period exceeds demand in that period, the product will be stored and a holding cost of $2 per unit is incurred. It is known that at the beginning of the period the company has 5 units of beginning inventory. In reality, not all products available in a period are able to meet demand in that period. To model this, it is assumed that only half of the available product can be used to meet demand in the period. In other words, the minimum number of products available in each period is double the demand for that period. Develop a suitable mathematical model for this case!arrow_forwardThe current solution to SureStep’s no-backloggingaggregate planning model requires a lot of firing. Runa one-way SolverTable with the firing cost as the inputvariable and the numbers fired as the outputs. Let thefiring cost increase from its current value to double that value in increments of $400. Do high firing costs even-tually induce the company to fire fewer workers?arrow_forwardThe operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and for each twin bed is $150. The manager’s goal is to maximize profits.What is the weekly profit when ordering the optimal amounts? Multiple Choice $54,000 $0 $42,000 $45,000 $30,000arrow_forward
- During the next four months, a customer requires,respectively, 500, 650, 1000, and 700 units of acommodity, and no backlogging is allowed (that is,the customer’s requirements must be met on time).Production costs are $50, $80, $40, and $70 per unitduring these months. The storage cost from one monthto the next is $20 per unit (assessed on ending inventory). It is estimated that each unit on hand at the endof month 4 can be sold for $60. Assume there is nobeginning inventory.a. Determine how to minimize the net cost incurred inmeeting the demands for the next four months.b. Use SolverTable to see what happens to the decisionvariables and the total cost when the initial inventoryvaries from 0 to 1000 in 100-unit increments. Howmuch lower would the total cost be if the companystarted with 100 units in inventory, rather than none?Would this same cost decrease occur for every100-unit increase in initial inventory?arrow_forwardA company produces three types of items. A singlemachine is used to produce the three items on a cyclicalbasis. The company has the policy that every item isproduced once during each cycle, and it wants to determinethe number of production cycles per year that will minimizethe sum of holding and setup costs (no shortages areallowed). The following data are given:Pi number of units of product i that could be producedper year if the machine were entirely devoted toproducing product iDi annual demand for product iKi cost of setting up production for product ihi cost of holding one unit of product i in inventoryfor one yeara Suppose there are N cycles per year. Assuming thatduring each cycle, a fraction N1of all demand for eachproduct is met, determine the annual holding cost andthe annual setup cost.b Let qi* be the number of units of product i producedduring each cycle. Determine the optimal value of N(call it N*) and qi*. c Let EROQi be the optimal production run size forproduct i if…arrow_forwardA firm knows that the price of the product it is ordering is going to increase permanently by X dollars. It wants to know how much of theproduct it should order before the price increase goes into effect. Here is one approach to this problem. Suppose the firm places one order for Q units before the price increase goes into effect.a. What extra holding cost is incurred by ordering Q units now?b. How much in purchasing costs is saved by ordering Q units now?c. What value of Q maximizes purchasing cost savings less extra holding costs?d. Suppose that the annual demand is 1000 units, the holding cost per unit per year is $7.50, and the price of the item is going to increase by $10. How large an order should the firm place before the price increase goes intoeffect?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,