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# Linear Programming

### Statistics: Linear Programming

LINEAR PROGRAMMING 1. Find the complete (including values for slack variables) optimal solution to this linear programming problem using. graphical method Min 5X + 6Y s.t. 3X + Y > 15 X + 2Y > 12 3X + 2Y > 24 X , Y > 0 2. Find the complete (including values for slack variabl

### Linear Programming Properties

1. Linear Programming Properties Which of the following statements IS true? a) An infeasible solution is one that must violate all constraints b) A feasible solution is one that must satisfy all constraints c) The objective function determines the shape of the feasible region d) An optimal solution does not have to lie o

### Transportation, Assignment, Linear Programming and Transhipment problems

Write the linear programming problem for this network. 2. Canning Transport is to move goods from three factories to three distribution centers. Information about the move is given below. Give the network model and the linear programming model for this problem. Source Supply Destination Demand A 200 X 50 B 100 Y 125

### Maximization linear programming model

A. Maximization Graph Solutions Given the following maximization linear programming model, which of the possible solutions provided below is NOT feasible? Maximize Z = 2X1 + 3X2 subject to: 4X1 + 3X2 < 480 3X1 + 6X2 < 600 a) X1 = 120 and X2 =0 b) X1 = 75 and X2 = 90 c) X1 = 90 and X2 = 75 d) X1 = 0 and X2 = 120 Ans

### Linear Programming, select extreme points

A. Minimization Graphical Solution Solve the following linear programming model graphically and select the set of extreme points that make up the solution: Minimize Z = 20X1 + 10X2 subject to: X1 + X2 < 12 2X1 + 5X2 > 40 X2 < 13 Note: The triplets are in the form of (X1 = ,X2 = , Z = ) a) (0, 12, 120), (0, 8, 80), (2

### Linear Programming - Maximizing Profit

1. The linear programming problem whose output follows is used to determine how many bottles of fire red nail polish (x1), bright red nail polish (x2), basil green nail polish(x3), and basic pink nail polish(x4) a beauty salon should stock. The objective function measures profit; it is assumed that every piece stocked will be so

### Linear Equations, Linear Programming, Matrix Inverses and Transposes and Basic Statistics

Hello, I would like for someone to check my answers for the problems that are highlighted in green to make sure that I have solved them correctly. However, there are several problems that are highlighted in yellow that I need help with. Could someone please provide the formula and break-down each step for those problems? Also, p

### Integer Linear Programming (ILP) : Formulation and Optimal Solution

Health Care Systems of Florida (HCSF) is planning to build a number of new emergency-care clinics in central Florida. HCSF management has divided a map of emergency-care clinics in central Florida. HCSF management has divided a map of the area into seven regions. They want to locate the emergency centers so that all seven reg

### Quantitative II

See attached For all linear programming problems, the implied non-negativity constraint is assumed. Don't forget to include this constraint if you are using Excel to solve any of these problems. 1. Linear Programming Properties Which of the following statements is not true? a) An infeasible solution violates all

### Linear Programming (4 Problems)

? Chapter 4 Problem 20 - Diet Mix Problem Anna Broderick is the dietitian for the State University football team and she is attempting to determine a nutritious lunch menu for the team. She has set the followng nutritional guidlens for each lunch serving: Between 1500 and 2000 caleries At least 5 mg of iron At least 20 b

### Linear Programming Refinery Blends Problem

Please help with the following problem involving linear programming. For part A it needs to be written out. For Eaxample: Maximize total profit Z = \$400C + \$100T subject to constraints: 8C + 10T <= 80 labor hours 2C + 6T <= 36 wood in lbs C <= 6 maximum demand for chairs C >0 and T > 0 for non negativity For pa

### Linear Programming Diet Mix: Dietitian Example

Ann Broderick is the dietitian for the State University football team, and she is attempting to determine a nutritious lunch menu for the team. She has set the following nutritional guidelines ... (see attached). Complete parts a and b. For part A it needs to be written out. For Eaxample: Maximize total profit Z = \$400C + \$

### Finding the Solution for a Linear Programming Example Problem

Please see attached for data. Brooks City has three consolidated high schools, each with a capacity of 1,300 students. The school board has partitioned the city into five busing districts each with different high school populations. The three schools are located in the central, west, and south districts. Some students must

### Network Models

12-7 Bechtold Construction is in the process of installing power lines to a large housing development. Steve Bechtold wants to minimize the total length of wire used, which will minimize his costs. The housing development is shown as a network in Figure 12.21. Each house has been numbered, and the distances between houses are g

### Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming: Sensitivity Analysis and Interpretation of Solution Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and grinder. The times (in minutes) required on each machine are as follows: Machine Component Shaper Grinder 1

### Simplex Method and Maximization Problem

Please see the attachment. Use the simplex method to solve the following maximization problem with the given tableau. Use the simplex method to solve. (You may need to use artificial variables)

### Linear Programming Problems and Network Flow Models

To use the balance-of-flow rule presented in this chapter, constraints for supply nodes must have negative RHS values. Some LP software packages cannot solve problems in which the constraints have negative RHS values. How should the balance-of-flow rules be modified to produce LP models that can be solved with such software pack

### Linear Programming: Model Formulation and Graphical Solution

The UN must evacuate an aid team and their belongings from Iraq. They can hire two types of planes to handle the evacuation. One is an Airbus 201 which can handle 25 passengers and 10 tons of cargo for \$800 per day. The other is a Boeing 179 which can handle 40 passengers and 4 tons of cargo at a cost of \$1000 per day. The ev

### Linear Programming : Maximizing Profit

Grand Lake Furniture Company makes two types of picnic tables, rectangular and hexagon. The hexagon table takes 4 hours to make and 2 hours to finish. the rectangular table takes 3 hours to build and 1 hour to finish. The company can devote 240 hours to building the tables and 100 hours to finish the tables. Each hexagon tab

### Linear Programming : Maximizing Profits

A California grower has a 50 acre farm on which to plant strawberries and tomatoes. The grower has available 300 hours of labor per week and 800 tons of fertilizer, and has contracted for shipping space for a maximum of 26 acres' worth of strawberries and 37 acres' worth of tomatoes. An acre of strawberries requires 10 hours of

### Linear Programming - Graphical and Computer Methods - Answer: Problem 6-36, Problem 7-16 & Problem 7-29

6-36 Ralph Janaro simply does not have time to analyze all of the items in his company's inventory. As a young manager, he has more important things to do. The following is a table of six items in inventory along with the unit cost and the demand in units. iDENTIFlcxnoN CODE' . UNIT COST (\$) DEMAND IN UNITS XXI 5.84 1,200

### Finite Mathematics - Linear Programming - Simplex Method

Karen Guarditlo has decided to invest a \$100,000 inheritance in govcrfltflcflt securities that earn 7% per year, municipal bonds that earn 6% per year, and mutual funds that earn an average of 10% per year. She will spend at least \$40,000 on government securities, and she wants at least half the inheritance 10 go to bonds and in

### Finite Mathematics - Linear Programming and then Simplex Method

Please do parts (a) and (b). Please see the attached file for the fully formatted problems. The Golden Hawk Manufacturing company wants maximize the profits on products A, B, and C. The contribution margin for each product follows: .... The production requirements and deprtmental capacities by departments, are as follows:

### Project Management exercises

Hello there, I need help with the problems attached. Please explain answers too. 1 Operations management is sometimes also as p___________ management and/or decision s_________ systems and/or management s________. 2 Examples of important OM methods and techniques include: a.   G___d   A______s b

### Economics-Total and Average costs

A firm has fixed costs of \$60 and variable costs as indicated in the table on the attached Excel spreadsheet. Complete the table and check the calculations. Total Product Total Fixed Cost Total Variable Cost 0 \$0 1

### Linear Programming : Constraints, Objective Function and Mimimizing Cost

Every January Santa tidies his workshop. Each toy in the workshop may be either stored for use next year, or taken apart and rebuilt next year, or thrown away and replaced next year. Storing a toy costs £1 and uses 8 units of storage space. Taking a toy apart and rebuilding it next year costs £3 and uses 2 units of storage

### Ranking Goals in Goal Programming

What does it mean to rank goals in goal programming? How does this affect the problem's solution?

### Linear Programming : Demand-side Constraints

1. Consider the following transportation problem: 1 2 Supply 1 5 6 100 2 4 2 200 3 3 6 150 4 9 7 50 Demand 250 250 How many supply-side constraints are there? Write the supply-side constraints. 2. Consider the following transportation problem: 1 2 Supply 1 5 6 100 2 4 2 200 3 3 6 150

### Linear Programming : Profit and Point of Change of Product Mix

The linear programming problem whose output follows is used to determine how many bottles of fire red nail polish (x1), bright red nail polish (x2), basil green nail polish(x3), and basic pink nail polish(x4) a beauty salon should stock. The objective function measures profit; it is assumed that every piece stocked will be sold.

### Linear Programming : Maximizing Profit ...

The production manager for the Whoppy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. The company operates one "8 hour" shift per day. Therefore, the production time is 480 minutes per day. During the production process, one of the main ingredients, syrup is limited to maximum produ