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# Linear Programming

### Linear Programming Problem : key information

Let A be a symmetric square matrix. Consider the linear programming problem Minimize C'X such that AX >= C and X >= 0 Prove that if X* satisfies AC*=C and X*>=0, then X* is an optimal solution.

### Linear Programming Problem

U Merchandise Corp. is planning to locate a store in a new shopping center being built in fast growing section of town. The project manager assigned to the project wants to establish some guidelines for the architect who will attempt to design a building layout to fit the companyâ??s specific needs. The guidelines are to incl

### Minimum production cost

A private Mom and Pops baseball company produces double aa quality baseballs and cletes. (Baseball shoes are called cletes). They have two different plants. One is in Manhattan the other in the Bronx. The one in Manhattan produces 600 double aa quality baseballs and 240 cletes an hour. The plant in the Bronx produces 240 dou

### IP problem and LP relaxation problem

Consider the IP problem given below. Minimize Summation (i=1 to 4) x_i, subject to x1 + x2 + x3 >= 1, x1 + x2 + x4 >= 1, x1 + x3 + x4 >= 1, x2 + x3 + x4 >= 1, x1, x2, x3, x4 belong to {0,1}, and the LP relaxation, which allows 0 <= x_i <= 1, for i = 1,2,3,4. Show that, (x1*,x2*,x3*,x4*) is an optimal solution to th

### Determine the optimal workforce schedule which meets specified personnel requirements and minimizes the cost.

The number of transaction requests received by a bank peaks around 1 PM. For efficient use of resources, the personnel available should therefore vary correspondingly. A variable capacity could be achieved by employing part-time personnel. The problem is to find the optimal workforce schedule that would meet the personnel req

### Simplex Method for Solving Nonstandard Problems

Please help with the following problem. Natsano has at most \$50,000 to invest in common stocks of two companies. He estimates that an investment in company A will yield a return of 10%, whereas an investment in company B, which he feels is a riskier investment, will yield a return of 20%. If he decides that his investment in

### Porsche Club Linear programming - optimal solution, profit, analysis

The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual racetracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Deegan Industries manufactures two types of roll bars for Porsches. Model DRB is bolt

### Operations Research Producing Wheat

Please find attached the questions.Thank you 1. Suppose that England, France, and Spain produce all the wheat, barley, and oats in the world. The world demand for wheat requires 125 million acres of land devoted to wheat production. Similarly, 60 million acres of land are required for barley and 75 million acres of land f

### Linear Programming problem

A company that has a two-year contract to haul ore from an open-pit mine to loading docks for shipping needs 200 additional trucks. Purchased trucks have a useful life of two years and a purchase cost of \$140,000 each. The company can lease trucks for \$80,000 per year (paid at the beginning of the year). Purchased trucks will be

### Stateline Shipping and Transport Company

I know that is an answer to this problem in the library, but I would like a more detail or perhaps a fresh view to this case. I am currently working with Microsoft Excel 2007. Any help would be really appreciated.

### Linear Programming Model (Transportation Problem)

Hospital transportation problem A large hospital has initiated a new procedure to ensure that patients receive their meal while the food is still as hot as possible. The hospital will continue to prepare the food in its kitchen but will now deliver it in bulk not individual servings to one of three new serv

### Linear Programming: Operations Research

See the attached file. Consider the following problem: A supermarket store manager needs to determine how much to stock of two brands of soda: PC and CC, for Super Bowl Sunday. The store needs to tell the suppliers how many "units" are available and the suppliers then stock the store with their product. Units consist of diff

### Linear Programming

Willis Eckley owns a fine woodworking company that manufactures and sells dining room table and chair sets. A table and chair set consists of one table and four chairs. Willis has established the following guidelines for production: 1. Tables and chairs shall not be sold individually, they shall only be sold in sets. 2. Tab

### Linear Programming - Maximum Profit

A store sells two kinds of bicycles, model A and model B. The store buys them unassembled from a wholesaler. Two employees are responsible for assembling the bicycles, and they are permitted to work no more than 6 hours each week to do this job. Working together to assemble model A, employee 1 works 3/4 hour and employee 2 works

### Question about Linear Programming - Maximum Profit

Muro manufacturing company makes two kinds of plasma screen TV's. It produces the flexscan set that sells for \$350 profit and the panoramic I that sells for \$500 profit. On the assembly line, the flexscan requires 5 hours, and the panoramic I takes 7 hours. The cabinet shop spends 1 hour on the cabinet for the flexscreen and 2

### Linear Programming Problem for Investment Alternatives

A young investor who has accumulated a large amount of money has sought advice from an investment counselor on how to invest some or all of the money. With the aid of the counselor, the investor has selected the following investment alternatives: common stock, treasury bills, AAA bonds, BBB bonds, income bonds, and negotiable

### Linear Programming Model for Maximization

[IV](20) The Golden Gate Cranberry Company purchases cranberries from local growers and makes cranberry sauce and cranberry juice. It costs \$0.70 to produce a can of cranberry sauce and \$0.95 to produce a bottle of cranberry juice. In order to present a representative marketing mix to its customers the company has made it a p

### Linear Programming Minimization Model

The famous Y. S. Chang Restaurant is open 24 hours a day. Waiters and busboys report for duty at 3 a.m., 7 a.m., 11 a.m., 3 p.m., 7 p.m., or 11 p.m., and each works an eight hour shift. the following table shows the minimum number of workers needed during the six periods into which the day is divided. PERIOD | TIME

### Linear programming model

The Hong family owns 410 acres of farmland along the Yangtze Valley on which they grow potatoes and rice. Each acre of potatoes costs \$165 to plant, cultivate, and harvest; each acre of rice costs \$220. The Hongs have a budget of \$77,000 for next year. If they plant over 200 acres of rice, worms will most likely destroy the crop

### Linear Programming: Red Brand Canners Case Study

See attached file. Red Brand Canners On Monday, September 13, 1999, Mitchell Gordon, Vice president of operations at Red Brand Canners, asked the controller, the sales manager, and the production manager to meet with him to discuss the amount of tomato products to pack that season. The tomato crop, which had been pur

### Linear Progamming

The Navy has 9,000 pounds of material in Albany, Georgia which it wishes to ship to three installations: San Diego, Norfolk and Pensacola. They require 4,000 2,500 and 2,500 pounds respectively. The following gives the shipping cost per pound for truck, railroad, amd airplane transit. Des

### Linear Programming - excel solver

The advertising manager at Cadillac wishes to run both television and magazine ads to promote the new Cadillac GTS in the greater Chicago area market. Each 30-second television ad will reach 30,000 viewers in the target age group of buyers 35 to 55 years old. Running one full page ad in Cool Driver magazine will reach 10,000 rea

### Linear Program help

The SMM Company,which is manufacturing a new instant salad machine, has \$350,000 to spend on advertising. The product is only to be test marketed initially in the Dallas area. The money is to be spent on an advertising blitz during one weekend( Friday, Saturday, Sunday) in January and SMM is limited to television advertising.

### Linear Programming

Triumph Trumpet Company makes two styles each of both trumpets and comets deluxe and professional models. Its unit profit on deluxe trumpets is \$80 and on deluxe comets is \$60. The professional models realize twice the profit of the deluxe models. Trumpets and comets are made basically from two mixtures of two different brass

### Perfect Competition

Firm PQR produces a product 'Alpha' under perfect competition market conditions. The cost function for the firm is: TC = 1500 + 200Q + Q^2 The market supply and demand equations for the product 'Alpha' in the perfect competition market are: QS = 40,000 + 60 P QD = 80,000- 40 P Based on the information given above, calcu

### Develop a linear programming model

Tots Toys makes a plastic tricycle that is composed of three major components: a handlebar-front wheel-pedal assembly, a seat and frame unit, and rear wheels. The company has orders for 12,000 of these tricycles. Current schedules yield the following information. Requirements Cost to Cost to Component Plastic Time Space M

### Simplex Method and Tableau Format: Maximize net daily profits

A company makes two types of antihistamine formulations: one for daytime use and one for nighttime use. The net profit for the daytime formulation is 20 cents per pill and the net profit for the nighttime formulation is 25 cents per pill. The formulations differ according to the quantities of two different ingredients: the dayti

### Simplex Method

A transport ship has three compartments for storing cargo: front, centre, and back. Each compartment has limits on the weight and volume of the cargo that can be carried, as summarized in the table below. To maintain an even keel in the water, care must be taken to insure that the relative weight of cargo stored in each compart

### Formulate a linear program

Problem: You work for a food company that makes two types of trail mix: Peak and TrailSnack. Each consists of some mix of peanuts, cashews, and raisins. You can obtain up to 100 kg/day of peanuts, 70 kg/day of cashews, and 60 kg/day of raisins. The Peak mix must contain at least 40% peanuts, at least 20% cashews and at least 20

### Formulate a linear programming model.

A manufacturing firm located in Chicago ships its product by railroad to Detroit. Several different routes are available, as shown in the attached diagram, referred to as a network. Each circle in the network represents a railroad junction. Each arrow is a railroad branch between two junctions. The number above each arrow