Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 4.3, Problem 11P
Summary Introduction
To determine: A plan that maximizes the number of weekend days off got by these employees.
Linear programming:
It is a mathematical modeling procedure where 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.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
A hospital emergency room requires different numbers of nurses on different days of the week. The number of full-time employees required to be working (i.e. not on call) each day is given in the table below.
Mon
Tue
Wed
Thu
Fri
Sat
Sun
18
15
12
13
20
28
22
Hospital rules require that nurses work four consecutive days, are on call for one day, and then receive two days off. The hospital wants to meet its daily requirements, while minimizing the number of nurses that must be on staff.
A. How many total nurses are needed to be on staff for the optimal solution?
B.Suppose the hospital is experiencing a budget crunch and needs to use the nurses' on call day to temporarily staff the emergency room.
How many nurses work on Thursday in the optimal solution?
C. Suppose the hospital has 40 nurses and is not allowed to hire or fire any employees, and cannot temporarily schedule nurses on their on call days. Determine a schedule that meets the daily requirements while maximizing the number…
11. The shadow price is calculated to be 5 for a less than or equal to constraint in a maximization LP problem, this means:
a. if the coefficient of the objective function is increase by 1 then the RHS for that constraint must be increased by 5
b. if the RHS for that constraint is increased by one then the optimal objective function value is increase by 5
c. if the RHS for that constraint is increased by 5 then the optimal objective function value is increase by 1
d. if the coefficient of the objective function is increase by 5 then the RHS for that constraint must be increased by 1
12. Sensitivity Analysis generally assumes
a. we are considering a change in two input data values at a time
b. are considering a change in only one input data value at a time
c. we are considering several change in several input data…
Suppose an assignment problem, where there are 3 employees who must perform 3 different tasks. The times (in hours) that employees take to perform each of the tasks is shown below. Each employee must perform only one task, and a task can only be performed by one employee. All employees are paid exactly the same wage per hour of work. Minimize the total time to make all tasks.
Task 1 Task 2 Task 3
Employee 1 154 29 40
Employee 2 18 137 12
Employee 3 94 13 31
How many variables does the problem have?
How many constraints does the problem have?
The objective function corresponds to:
Chapter 4 Solutions
Practical Management Science
Ch. 4.2 - Prob. 1PCh. 4.2 - Prob. 2PCh. 4.2 - Prob. 3PCh. 4.2 - Prob. 4PCh. 4.2 - Prob. 5PCh. 4.2 - Prob. 6PCh. 4.3 - Prob. 7PCh. 4.3 - Prob. 8PCh. 4.3 - Prob. 9PCh. 4.3 - Prob. 10P
Ch. 4.3 - Prob. 11PCh. 4.3 - Prob. 12PCh. 4.4 - Prob. 13PCh. 4.4 - Prob. 14PCh. 4.4 - Prob. 15PCh. 4.4 - Prob. 16PCh. 4.4 - Prob. 17PCh. 4.4 - Prob. 18PCh. 4.4 - Prob. 19PCh. 4.5 - Prob. 20PCh. 4.5 - Prob. 21PCh. 4.5 - Prob. 22PCh. 4.5 - Prob. 23PCh. 4.5 - Prob. 24PCh. 4.5 - Prob. 25PCh. 4.6 - Prob. 26PCh. 4.6 - Prob. 27PCh. 4.6 - Prob. 28PCh. 4.6 - Prob. 29PCh. 4.7 - Prob. 30PCh. 4.7 - Prob. 31PCh. 4.7 - Prob. 32PCh. 4.7 - Prob. 33PCh. 4.7 - Prob. 34PCh. 4.7 - Prob. 35PCh. 4.7 - Prob. 36PCh. 4.7 - Prob. 37PCh. 4.7 - Prob. 38PCh. 4.7 - Prob. 39PCh. 4.7 - Prob. 40PCh. 4.8 - Prob. 41PCh. 4.8 - Prob. 42PCh. 4.8 - Prob. 43PCh. 4.8 - Prob. 44PCh. 4 - Prob. 45PCh. 4 - Prob. 46PCh. 4 - Prob. 47PCh. 4 - Prob. 48PCh. 4 - Prob. 49PCh. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - Prob. 53PCh. 4 - Prob. 54PCh. 4 - Prob. 55PCh. 4 - Prob. 56PCh. 4 - Prob. 57PCh. 4 - Prob. 58PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61PCh. 4 - Prob. 62PCh. 4 - Prob. 63PCh. 4 - Prob. 64PCh. 4 - Prob. 65PCh. 4 - Prob. 66PCh. 4 - Prob. 67PCh. 4 - Prob. 68PCh. 4 - Prob. 69PCh. 4 - Prob. 70PCh. 4 - Prob. 71PCh. 4 - Prob. 72PCh. 4 - Prob. 73PCh. 4 - Prob. 74PCh. 4 - Prob. 75PCh. 4 - Prob. 76PCh. 4 - Prob. 77PCh. 4 - Prob. 78PCh. 4 - Prob. 79PCh. 4 - Prob. 80PCh. 4 - You want to take out a 450,000 loan on a 20-year...Ch. 4 - Prob. 82PCh. 4 - Prob. 83PCh. 4 - Prob. 84PCh. 4 - Prob. 85PCh. 4 - Prob. 86PCh. 4 - Prob. 87PCh. 4 - Prob. 88PCh. 4 - Prob. 89PCh. 4 - Prob. 90PCh. 4 - Prob. 91PCh. 4 - Prob. 92PCh. 4 - Prob. 93PCh. 4 - Prob. 94PCh. 4 - Prob. 95PCh. 4 - Prob. 96PCh. 4 - Prob. 97PCh. 4 - Prob. 98PCh. 4 - Prob. 99PCh. 4 - Prob. 100PCh. 4 - Prob. 101PCh. 4 - Prob. 102PCh. 4 - Prob. 103PCh. 4 - Prob. 104PCh. 4 - Prob. 105PCh. 4 - Prob. 106PCh. 4 - Prob. 107PCh. 4 - Prob. 108PCh. 4 - Prob. 109PCh. 4 - Prob. 110PCh. 4 - Prob. 111PCh. 4 - Prob. 112PCh. 4 - Prob. 113PCh. 4 - Prob. 114PCh. 4 - Prob. 115PCh. 4 - Prob. 116PCh. 4 - Prob. 117PCh. 4 - Prob. 118PCh. 4 - Prob. 119PCh. 4 - Prob. 120PCh. 4 - Prob. 121PCh. 4 - Prob. 122PCh. 4 - Prob. 123PCh. 4 - Prob. 124PCh. 4 - Prob. 125PCh. 4 - Prob. 126PCh. 4 - Prob. 127PCh. 4 - Prob. 128PCh. 4 - Prob. 129PCh. 4 - Prob. 130PCh. 4 - Prob. 131PCh. 4 - Prob. 132PCh. 4 - Prob. 133PCh. 4 - Prob. 134PCh. 4 - Prob. 135P
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
- 1. The Kalo Fertilizer Company makes a fertilizer using two chemicals that provide nitrogen, phosphate, and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, while a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phosphate, and 1 ounce of potassium. Ingredient 1 costs $3 per pound, and ingredient 2 costs $5 per pound. The company wants to know how many pounds of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 20 ounces of nitrogen, 36 ounces of phosphate, and 2 ounces of potassium while minimizing cost. REQUIRED: a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis.arrow_forwardMete makes his living buying and selling corn. On January 1, he has 50 tons of corn and 1000 TL. On the first day of each month Mete can buy corn at the following prices per ton. January: 300 TL, February: 350 TL, March: 400 TL, April: 500 TL. On the last day of each month Mete can sell corn at the following prices per ton: January: 250 TL, February: 400 TL, March: 350 TL, April: 550 TL. Mete stores his corn in a warehouse that can hold at most 1100 tons of corn. He must be able to pay cash for all corn at the time of purchase. How Mete can maximize his cash on hand at the end of April. Which of the following is the correct objective function for the given statement? Please use (Xi = Tons of corn purchased at the beginning of month i.; Yi = Tons of corn sold at the end of month i.)arrow_forwardYou are moving away from Bloomington and need to load a truck. The items that will go on the truck must all be packed in boxes. The size (in cubic feet) of each item and each available box are listed in the file P06_95.xlsx. For example, the first item requires 78 cubic feet, and the first box can hold 116 cubic feet of stuff. Develop a linear integer model to find the minimum amount of cubic feet needed to pack all items in boxes. Assignments: Item Box 1 2 3 4 5 6 7 8 9 10 11 Total Cubic Feet: $ Box packing data Item to pack Cubic feet 1 78 2 63 3 87 4 56 5 88 6 56 7 75 8 62 9 52 10 71 11 54 Box Cubic feet 1 116 2 112 3 119 4 167 5 90 6 166 7 112 8 109arrow_forward
- A dietitian wishes to plan a meal around three foods. The percentages of the daily requirements of proteins, carbohydrates, and iron contained in each ounce of the three foods are summarized in the following table: Food 1 Food 2 Food 3 Protein (%) 10 6 8 Carbohydrates (%) 10 12 6 Iron (%) 5 4 12 The dietitian desires each meal to meet exactly the daily requirement of proteins, carbohydrates, and iron (100%) of each.(i) Using the information in the table above, write a system of three equations.(ii) Write the system in matrix form Ax= b .(iii) Using the Inverse Method, determine how many ounces of each food should the dietitian include in the meal to meet the daily requirements exactlyarrow_forward1. The JAV Company manufactures two types of lamps; Special lamp and 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 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 machine, The company's machine 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 bulb is limited to 200 units. The contribution to profit of each special lamp and regular lamp are P400 and P360 respectively. How many units of the special lamp and regular lamp should be produced per production period in order to maximize the profit? a) What will happen to the optimal solution if the unit profit on x increase by 300? b) what will happen happen to the optimal solution if the unit profit on y…arrow_forward1. The JAV Company manufactures two types of lamps; Special lamp and 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 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 machine, The company's machine 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 bulb is limited to 200 units. The contribution to profit of each special lamp and regular lamp are P400 and P360 respectively. How many units of the special lamp and regular lamp should be produced per production period in order to maximize the profit? a) What will happen to the optimal solution if the unit profit on x increase by 300? b) what will happen happen to the optimal solution if the unit profit on y…arrow_forward
- 3. Atlas Fertz Corp. makes a fertilizer using two chemicals that provide nitrogen, phosphate, and potassium. A kilogram of ingredient 1 contributes 150 grams of nitrogen and 90 grams of phosphate, while a kilogram of ingredient 2 contributes 30 grams of nitrogen, 90 grams of phosphate, and 15 grams of potassium. Ingredient 1 costs P300 per kilograms , and ingredient 2 costs P500 per kilogram. The company wants to know how many kilogram of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 600 grams of nitrogen, 1080 grams of phosphate, and 60 grams of potassium while minimizing cost. a. Formulate the LP model for this problem. b. Develop a spreadsheet model and solve using Excel Solver. What is the optimal solution?arrow_forwardA production department requires different numbers of full-time employees on different days of the week. The number of full-time employees required on each day is given (see Table). Union rules state that each full-time employee must work five consecutive days and then two days off. For example, if an employee works Monday to Friday, he/she will be off on Saturday and Sunday. Suppose that the production department wants to meet its daily requirements using only full-time employees. Formulate an LP that the production department can use to minimize the number of full time employees who must be hired. Day # of Full-Time Employees Required Monday 17 Tuesday 13 Wednesday 15 Thursday 19 Friday 14 Saturday 16 Sunday 11 a) Formulate an LP that the production department can use to minimize the total cost instead of the number of employees. (Let ci: the cost of workers who start work on day i) b) Suppose that the production department can meet its daily requirements using both fulltime and…arrow_forward2 ABCD company is an office equipment company that produces two types of desks: standard and deluxe. Deluxe desks have oak tops, more expensive hardware, and require additional time for finishing and polishing. Standard desks require 80 square feet of pine and 10 hours of labor, while deluxe desks require 60 square feet of pine, 18 square feet of oak, and 16 hours of labor. For the next week, the company has 5,000 square feet of pine, 750 square feet of oak, and 400 hours of labor available. Standard desks net a profit of $150, while deluxe desks net a profit of $320. All desks can be sold to national chains shops. Instructions: If the spreadsheet and Excel Solver results are given to you as follows (see Table 1 below), address the following questions: What are your Binding Constraints? What is your Optimum profit [hint: maximized profit]? What are your slack values for Pine, Oak, and Labor? Looking at the Shadow prices, how much would the objective profit increase by if you were to…arrow_forward
- Example 1. The Big M Method solve LP with mixed constraints Minimize: Z = 4x1 + 2x2 + x3 Subject to: 2x1 + 3x2 + 4x3 ≤ 14 3x1 + x2 + 5x3 ≥ 4 x1 + 4x2 + 3x3 ≥ 6 x1, x2, x3≥ 0arrow_forwardIn the Great Threads model, we didn’t constrain the production quantities in row 16 to be integers, arguing that any fractional values could be safely rounded to integers. See whether this is true. Constrain these quantities to be integers and then run Solver. Are the optimal integer values the same as the rounded fractional values in Figure 6.12?arrow_forward
arrow_back_ios
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,