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# Linear Programming

### Consider the following linear program:

Consider the following linear program: Min 2A+2B s.t. 1A+3B&#8804;12 3A+1B&#8805;13 1A-1B=3 A,B&#8805;0 a. Show the feasible region. b. What are the extreme points of the feasible region? c. Find the optimal solution using the graphical solution procedure.

### Linear programming

1. Which of the following mathematical relationships could be found in a linear programming model? And which could not (why)? a. -1A + 2B &#8804; 70 b. 2A - 2B = 50 c. 1A - 2B^2 &#8804; 10 d. 3 &#8730; A + 2B &#8805; 15 e. 1A + 1B = 6 f. 2A + 5B + 1AB &#8804; 25 2. Find the solutions t

### Quantitative Methods - Linear Program Graphic Solution Procedure

1. For the linear program: Max 2A + 3B s.t. 1A + 2B &#8804; 6 5A + 3B &#8804; 15 A,B &#8805; 0 Find the optimal solution using the graphical solution procedure. What is the value of the objective function at the optimal solution? 2. Solve the following linear program using the graphical solution procedure.

### Linear Programming

The lakeside boatwork is planning to manufacture three types of molded fiberglass recreation boats, a fishing (bass0 boat, a ski boat, and a small speedboat. The estimated selling price and variable cost for each type of boat are summarized in the following table Bass \$12,500 \$23,000 Ski 8,5000 18,000 speed

### The Jones Furniture company produces tables and chairs from two resources: labor and wood. The company has 80 hours of labor and 34 pounds of wood available each day...

The Jones Furniture company produces tables and chairs from two resources: labor and wood. The company has 80 hours of labor and 34 pounds of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 pounds of wood to produce, whereas a table requires 10 hours of labor and 7 p

### Khan manufacturing produces two popular grades of commercial carpeting among its many other products.

Khan manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Khan needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade A carpet uses 50 units of synthetic fiber, requires 25 hours of production tim

### A restaurant sells ice cream and frozen yogurt.

A restaurant sells ice cream and frozen yogurt. The restaurant makes one order for ice cream and frozen yogurt per week, and the store has enough freezer space for 110 gallons of both products. A gallon of froze yogurt costs \$0.85 and a gallon of ice cream costs \$0.95, and the restaurant budges \$90 a week for these products. The

### Algebra - Lenear Programming

A restaurant sells ice cream and frozen yogurt. The restaurant makes one order for ice cream and frozen yogurt per week, and the store has enough freezer space for 110 gallons of both products. A gallon of froze yogurt costs \$0.85 and a gallon of ice cream costs \$0.95, and the restaurant budges \$90 a week for these products. The

### Linear programming model

The Smith family owns 405 acres of farmland in Virginia on which they grow corn and tobacco. Each acre of corn costs \$110 to plan, cultivate, and harvest; each acre of tobacco costs \$215. The Smith family budget \$55,000 for next year. The government wants to limit the number of acres of tobacco that can be planted to 100 acres.

### Quantitative Decision Making

Linear Programing Shale-Bituminous Processors Shale Bituminous Processors (SBP) is a medium-sized oil company. Using its own patented process, it produces low- and high-sulphur crude from coal and shale. These oils are used by refiners who process them into products such as gasoline, jet fuel, industrial lubricating oils

### Linear Programming Question

Looking for assistance in setting up the problem. I am trying to establish the constraints and the table for solver. (See attached) Transportation System A company which manufactures product in five plants ships locally using its own transportation system, but has orders which must be sent to locations too far to be servi

### Transportation Problem: Interpretation of output from Management scientist

I have a study problem that I need help with. We're studying network models and linear programming models related to transshipment and transportation. Here is the specific problem I need help with: ----------------------------------------------------------------------- The following table shows the unit shipping co

### Linear Programming Problem - Simplex Method..

Solve by Simplex Method: Maximize P=X1 + 2X2 Subject 2X1 + 2X2 &#8804; 8 4X1 + 2X2 &#8804; 12 -3X1 + 5X2 &#8804; 15 X1 &#8804; 4 where X1, X2 &#8805; 0

### Linear Programming Problem - Simplex Method..

Solve the following linear program either by hand using the simplex procedure or by using excel solver. Maximize P = 3X1 + 2X2 Subject to 10X1 + 2X2 &#8804; 20 X1 + X2 &#8804; 6 where X1, X2 &#8805; 0

### Linear Programming to Determine Largest Profit Possible

1. The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: Carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm

### Maximization Applications - 1. A manufacturer of bicycles builds one, three, and ten-speed models. The bicycles are made of both aluminum and steel. The company has available 91,800 units of steel and 42,000 units of aluminum. ...

In the following exercise, (a.) use the simplex method to solve the problem and (b.) explain what the values of the slack variables in the optimal solution mean in the context of the problem. 1. A manufacturer of bicycles builds one, three, and ten-speed models. The bicycles are made of both aluminum and steel. The company

### Linear Programming

Max Z = \$0.30x + \$0.90y Subject to : 2x + 3.2y 160 4x + 2y 240 y 40 x, y Solve for the quantities of x and y which will maximize Z. What is the value of the slack variable associated with constraint 2? Use Lingo10 or QM to solve. Include your solution screen shots

### Linear Programming Problem

Max 8X + 7Y s.t. 15X + 4Y < 75 10X + 7Y < 70 X + Y < 8 X, Y > 0 a.Use a graph to show each constraint and the feasible region. b.Identify the optimal solution point on your graph.What are the values of X and Y at the optimal solution? c.What is the optim

### Linear programming model

See also attachment for formatting. 1. Solve the following linear programming model by using the computer: Maximize Z = 5x1 + 8x2 Subject to 3x1 + 5x2 &#8804; 50 2x1 + 4x2 &#8804; 40 x1 &#8804; 8 x2 &#8804; 10 x1, x2 &#8805; 0 2. Solve the following linear programming model by using the computer:

### (1) Graph the following systems of inequalities; find the solution region and the vertices. (2) Solve the following linear programming graphically. ... [See the Attached Questions File.]

[See the Attached Questions File.] (1) Graph the following systems of inequalities; find the solution region and the vertices. (2) Solve the following linear programming graphically. ... (5) (a) A nutritionist is designing a new breakfast cereal using wheat germ and enriched oat flour as the basic ingredients. Each ounce of wh

### (1) Graph the following systems of inequalities; find the solution region and the vertices. (2) Solve the following linear programming graphically. ... [See the Attached Questions File.]

[See the Attached Questions File.] (1) Graph the following systems of inequalities; find the solution region and the vertices. (2) Solve the following linear programming graphically. ... (5) (a) A nutritionist is designing a new breakfast cereal using wheat germ and enriched oat flour as the basic ingredients. Each ounce of wh

### Linear Programming An oil company tries to maximize its profit by optimal decisions regarding the selling of different products. Some issues should be considered for example limitted emount of products and etc. Find an LP model which aims to maximize the profit.

How do I set up the problem and find the maximum profit? I have tried for hours but still confused. Linear programming The Grand Strand Oil Company The Grand Strand Oil Company produces regular and premium gasoline for independent service stations in the southeastern United States. The Grand Strand

### The Live Wright Medical Supplies Company has a total of 12 salespeople

The Live Wright Medical Supplies Company has a total of 12 salespeople it wants to assign to three regions-the South, the East, and the Midwest. A salesperson in the South earns \$600 in profit per month for the company, a salesperson in the East earns \$540, and a salesperson in the Midwest earns \$375. The southern region can hav

### Making Predictions from Data

(a) Plot the data on U.S. general aviation shipments. (b) Describe the pattern and discuss possible causes. (c) Would a fitted trend be helpful? Explain. (d) Make a similar graph for 1992-2003 only. Would a fitted trend be helpful in making a prediction for 2004? (e) Fit a trend model of your choice to the 1992-2003 data.

### Optimal value of the objective function

1. Consider the following linear programming problem Max 8X + 7Y s.t. 15X + 5Y < 75 10X + 6Y < 60 X + Y < 8 X, Y ³ 0 What is the optimal value of the objective fu

### Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of U shares of U.S. Oil and H shares of Huber Steel. The annual return for U.S. Oil is \$3 per share and the annual return for Huber Steel is \$5 per share. U.S. Oil sells for \$25 per share and Huber Steel sells for \$50 per share. The portfolio has \$80,000 to be invested. The portfolio risk index (0.50 per share U.S. Oil and 0.25 per share for Huber Steel) has a maximum of 700. In addition, the portfolio is limited to a maximum of 1000 shares of U.S. Oil. The linear programming formulation that will maximize the total annual return of the portfolio is as follows: Max z = 3U + 5H Subject to: 25U + 50H &#8804; 80,000 Funds available 0.50U + 0.25H &#8804; 700 Risk maximum 1U &#8804; 1000 U.S. Oil maximum U, H &#8805; 0 What is the optimal solution, and what is the value of the total annual return?

Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of U shares of U.S. Oil and H shares of Huber Steel. The annual return for U.S. Oil is \$3 per share and the annual return for Huber Steel is \$5 per share. U.S. Oil sells for \$25 per share and Hube

### Quantitative Methods

Solve linear programming problem. See the attached document for proper formatting. Week 7 Hartley's makes furniture. The time required for each item is listed below. Find the mix of products and sensitivity report to make the highest profit for Harley's. Chairs Tables Bookcases Available Assemb

### Quantitative Methods - Linear Programming (Maximization)

7-18 For the linear program Max 4A + 1B s.t. 10A + 2B <= 30 3A + 2B <= 12 2A + 2B <= 10 A, B >= 0 a. Write this problem in standard form. b. Solve the problem using the graphical solution procedure. c. What are the values of the three slack variables at optimal solution? Please provide detailed instruc

### Formulate A Linear Programming Model - Universal Claims Processors processes insurance claims for large national insurance companies. , Most claim processing is done by a large pool of computer operators, some of ...

Universal Claims Processors processes insurance claims for large national insurance companies. , Most claim processing is done by a large pool of computer operators, some of whom are permanent and some of whom are temporary. A permanent operator can process 16 claims per day, whereas a temporary operator can process 12 per day,

### Linear Programming Problem - Maximization..

Food and clothing are shipped to Victims of a natural disaster. Each carton of food will feed 13 people while each carton of clothing will help 6 people. Each 20 cubic foot box of food weighs 40 pounds and each 5 cubic foot box of clothing weighs 25 pounds. The commercial carriers transporting food and clothing are bound by the