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# Linear Programming

### Linear Programming and Simplex Methods : Minimization

The linear programming problem. Minimize 5x - y subject to: -2x - 2y < 12 -3x + 2y > 0 x > 0, y > 0 is equivalent to the linear programming problem: a. Maximize 5x - y subject to: -2x -2y < 12 3x - 2y < 0 x > 0, y > 0 b. Maximize 5x-y subject to: -2x -2y < 12 -3x + 2y > 0 x >

### Linear Programming and the Simplex methods : Surpluses

Consider the following linear programming problem: A workshop of Peter's Potters makes vases and pitchers. Profit on a vase is \$3.00; profit on a pitcher is \$4.00. Each vase requires ½ hour of labor, each pitcher requires 1 hour of labor. Each item requires 1 unit of time in the kiln. Labor is limited to 4 hours per day a

### Linear Programming : Writing Constraints and Maximizing Profit

The Chop is the manufacturer of the store brand of hatchets and axes sold by various home hardware supply stores. Each item consists of a hickory handle produced in the local processing facility and a steel blade forged and polished in the local machine shop. These two items are then transported to an assembly area where the b

### Linear Programming with Excel

Acme estimates it costs \$1.50 per month for each unit of this appliance carried in inventory (estimated by averaging the beginning and ending inventory levels each month). Currently, Acme has 120 units in inventory on hand for the product. To maintain a level workforce, the company wants to produce at least 400 units per month.

### Network Model Transportation Problem: Supply and Demand

Please help with the following problem. 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. Supply at Source Demand at Destination 200 A

### Linear Programming of Transportation and Shipment Problem

I need some help with a network diagram and formulation of the linear programming model. A company ships computers from factories to stores per week as follows: Factory #1 produces 400 computers per week. Factory #2 produces 200 computers per week. Factory #3 produces 150 computers per week. Store #1 needs 200 computers

### Linear Programming : Simplex Method in Tableau Form

The following problem is something that needs to be put into tableau iterations, but I'm not sure of my answers on it... I'm catching on slowly, but would like to have something to use to check my work... This is a homework problem, but the homework is graded on participation, not correctness in this distance learning class.

### Maximum-Minimum Theorem : Continuity and Bounded Functions

(d) Does the conclusion of the Maximum-Minimum Theorem always hold for a bounded function f : R --> R that is continuous on R? Prove or give a counterexample. (a) Fix a, b E R, a < b. Prove that if f [a, b] -->R is continuous on [a, b] and f(x)&#8800;0 for all x E [a, b], then 1/f(x) is bounded on [a, b]. (b) Find a, b E R, a

### Maximum-Minimum Theorem, Limits, Continuity

1) Let f, g be defined on R and let c in R. Suppose that lim f = b and that g is continuous at b. Show that lim g 0 f = g(b) Note: R: real numbers g 0 f means composition of f and g 2) Let A = [0, 1) U (1,2]. Let B = [0, 1] U [2, 3]. Does the conclusion of the maximum-minimum theorem always hold for a function f: A

### Linear Programming: Maximizing Profit for The Outdoor Furniture Corporation

The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its 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

### Linear Programming Models: Graphical method problems

Please help with the following problem. The dean of the Western College of Business must plan the school's course offering for the Fall semester. Students' demands make it necessary to offer at least 30 undergraduate and 20 graduate courses in the term. Faculty contracts also dictate that at least 60 courses be offered in to

### Linear Programming Models: Graphical Methods and Risk Analysis

The winner of the Texas Lotto has decided to invest \$50,000 per year in the stock market. Under consideration are stocks for a petrochemical firm and a public utility. Although a long-range goal is to get the highest possible return, some consideration is given to the risk involved with the stocks. A risk index on a scale of 1-1

Please help with the following problem. A candidate for mayor in a small town has allocated \$40,000 for last-minute advertising in the days preceding the election. Two types of ads will be used: radio and television. Each radio ads costs \$200 and reaches an estimated 3,000 people. Each television ad costs \$500 and reaches an

### Linear Programming : Decision variables, Constraints and Objective Function

Saudi Oil Company has 5000 barrels of Type A oil and 10000 barrels of Type B oil. The company sells two products: Gasoline and Heating Oil. Both products are produced by combining Type A and Type B oil. The "quality level" of Type A oil is 10 and that of Type B oil is 5. Gasoline must have an average quality level of at least 8

### Linear Programming : Objective Functions, Constraints and Optimal Solutions

PROBLEM 1 1. Use this graph to answer the questions. Maximize 28X + 35Y Subject to: 12X + 15Y < 180 15X + 10Y &#8805; 150 3X - 8Y < 0 X , Y > 0 a. What is the feasible region (I, II, III, IV, or V)? b. Which point (A, B, C, D, or E) is optimal?

### Modeling Problem: Two Decision Variables (Linear Programming / Optimal Solution)

A manufacturer of excercise equipment will begin production of two types of machines: Body Plus 100 and Body Plus 200. The Body Plus 100 consists of a frame unit, a press station, and a pec-dec station. each frame produced uses 4 hours of machining and welding time and 2 hours of finishing and painting time. Each press stat

### Linear Programming : Simplex Method (5 Problems)

1. Consider the simplex tableau x y u v w M [ 1 0 3 0 0 0 | 10] [ 0 0 1 0 1 0 | 0] [ 0 1 -6 0 0 0 | 3] [ 0 0 8 1 0 0 | 7] [

### Linear Programming : Simplex Method, Pivoting and Maximizing Values

1. Consider the following linear programming problem: Maximize 10x + 7y subject to: X + 3y (less than or equal to symbol) 10 2x -y (less than or equal to symbol) 8 x (greater than or equal to symbol) 0, y (greater than or equal to symbol) 0 The initial simplex tableau is: (for choices, please see attachment)

### A company makes a single product on two separate production lines, A and B.

I have one last work problem where my solution just doesn't to be correct Set up the objective function and constraints and then solve for the following: A company makes a single product on two separate production lines, A and B. The company's labor force is equivalent to 1,000 hours per week, and it has \$3,000 outlay week

### Linear Programming: Minimize z=6x+2y

Minimize z=6x+2y subject to constraints x+y>40, x+y>16, 4x+2y>48, x>0, y>=0

### Linear Programming - Simplex Methods (Finite Mathematics)

1. The feasible set of a certain linear programming problem is given by the following system of linear inequalities. x + 3y (less than or equal to symbol) 6 x - y (less than or equal to symbol) 2 - 5x + y (less than or equal to symbol) 2 Without graphing this set, determine which of the

### Linear programming

A cargo airplane operated by has three compartments for storing cargo: front, center, and back. These compartments have capacity limits on both weight and space, as summarized below: Compartment Weight Capacity (tons) Space Capacity (cu.ft.) Front Center Back 12 13 10 7,000 9,000 5,000 To ensure proper weight

### Finite Elements in Two Lines

PLEASE SHOW HOW TO WORK PROBLEMS 1.If two lines intersect in more than one point, then they are a. parallel b. inconsistent c. the same d. unique e. none of the above 2.Consider the following linear programming problem. A coffee merchant sells two blends of coffee. Each pound of blend A contains 80% Mocha Java and 20% J

### Linear programming

The problem is in the attachment file. Thank you. Optimization The Sentry Lock Corporation manufactures a popular commercial security lock at plans in Macon, Louisville, Detroit, and Phoenix. The per unit cost of production at each plant is \$35.5, \$37.5, \$39, and \$36.25, respectively, while the annual production capaci

### Linear Programming for a Management Scientist

Baseball Inc produces Regular gloves and Catcher?s mitt. The linear programming problem is listed below: Max 5R + 8C s.t. R + 3C < or equal to 1800 Cutting dept 3R + 2C < or equal to 1800 Finishing dept R + 2C < or equal to 800 Packaging dept R, C, > or equal to 0 The computer solution obtained using the Mana

### Application of Linear Programming to Financial Budgeting and the Costing of Funds

Can anyone tell me "linear programming: direct and dual relations" are about in plain English, please? Especially for "Fig 1-Schema for a simple warehouse model", please tell me how the model works. Thank you. Please see the attachments for more details.

### Linear Programming

Problem # 2 EM manufactures two lightweight motocycles designed for easy handling. The EZ Rider and the Lady Sport. Each EZ Rider engine requires 6hrs of manufacturing time and each Lady Sport requires 3 hrs of manufacturing time. EM produces the engines for both model at the DesMoines plant. The Des Moines plant has 2100 h

### Transportation Minimum-Cost Model Problems

The problem is posted in the attachment. Thank you. Transportation Problem Set 1. Consider a transportation problem with 4 sources and 3 demand points. (a) Write the min-cost model in full (without using &#8721; notation). (b) Draw the network. (c) Construct the standard data table. 2. Consider a transportation prob

### Linear Programming Formulation Problems

Linear Programming Formulation Problem Set (Show all works.) 1. A farmer can purchase 3 kinds of feed for his stock, with various percentages of each of 4 nutrients, called A, B, C, and D. A mixture of feeds gives proportional amounts of nutrients. The following table gives the minimum daily requirements (lb), cost (¢ / lb

### Define appropriate vectors and matrices to formulate the LP problem as a set of matrix equations.

A fertiliser company has available 80 tonnes of nitrate and 50 tonnes of phosphate to use during the coming week to produce three different types of lawn fertilisers. The mixture ratios and profit are given in the table below . The manager of the company wants to maximise profit from the raw materials currently available and dec