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# Linear Programming

### Linear Programming

1. A company must meet on time the following demands: quarter 1, 3000 units; quarter 2, 2000 units; quarter 3, 4000 units. Each quarter, up to 2700 units can be produced with regular-time labor, at a cost of \$40 per unit. During each quarter, an unlimited number of units can be made with overtime labor, at a cost of \$60 per un

### Calculations with integer variables

During each four hour period, the Okinawa police force requires the following number of on-duty police officers: eight from midnight to 4 am; seven from 4 am to 8 am; six from 8 am to noon; six from noon to 4 pm; five from 4 pm to 8 pm; and four from 8 pm to midnight. Each police officer works two consecutive four-hour shifts.

### Linear programming in excel 2007

Here is the problem: The offensive coordinator for the Chicago Bears football team is preparing a game plan for the upcoming game against the Green Bay Packers. A review of game tapes from previous Bears-Packers games provides data on the yardage gained for run plays and pass plays. Data show that when the Bears run against t

### Linear Programming using the Corner Points Method

Find the optimal solution using the Corner Points method. Min 2x + 2y Subject to x + y > 5 x + 2y < 8 x, y > 0

### positive integers programming

Formulate the following problem as an integer program. DO NOT SOLVE. A hiker has to load three items [food, water, tent] into his shoulder bag for his overnight trip. The weight per unit is food water tent 2 5 15 The value of these goods is food water Tent 8 10 25 However, he will only carry a tent if he

### Integer programming: Branch and bound splitting

Consider the integer program Max 5x + 2y s.t. 2x + 2y <=9 3x+y <=11 Nonnegative integers The optimal noninteger solution is x = 3.25 and y = 1.25 with optimal value 18.75. Solve the problem using branch and bound splitting on y first.

### 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.

### Characterize the linear programming problem.

4. Determine whether the following linear programming problem is infeasible, unbounded, or has multiple optimal solutions. Draw a graph and explain your conclusion. Maximize 20x + 5y Subject to: 2x + y > 15 x + y < 5

### 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

### optimal investment strategy for the row player

You have inherited \$10,000 just prior to a presidential election and wish to invest it in solar energy and oil stocks. An investment advisor provides you with a payoff matrix that indicates your probable 4-year gains, depending on which party comes into office. How should you invest your money so that you would have the largest

### 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

### Standard Minimization Problems

Can you please solve in detail the following equations with step by step up to the final simplex tableau; Mininize C=-2x-3y subjext to 3x+4y<=24 7x-4y<=16 x>=0, y>=0.

### 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

### Transportation Linear Programming Problem

TRANSPORTATION ASSIGNMENT The Marion Fruit Company has orange groves at three different sites throughout central Florida. It also has four plants for turning fruit into orange juice concentrate. The fruit must be picked and transported from the groves to the concentrate plant. The transportation costs depend directly upon the

### 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

### Why is it not an LP problem?

The following problem is not an LP problem. Maximize uw -vw - ut + vt, subject to u + v <= 10, w + t <= 15, u >= 2, 2u - v <= 2, t >= 5, u, v, w, t > 0. Why is it not an LP problem? Upon further inspection, however, this problem can be solved using LP methods. Solve this problem.

### 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 Programmin maximization problem, shadow price

Consider the following problem. Maximize Z = 3x1 + 2x2, subject to x1 â?¤ 4 (resource 1) x1 + 3x2 â?¤ 15 (resource 2) 2x1 + x2 â?¤ 10 (resource 3) and x1 â?¥ 0, x2 â?¥ 0, where Z measures the profit in dollars from the two activities and the right-hand sides are the number of units available of the respective r

### 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

### Simplex method-Maximization

A baker has 150 units of flour, 90 of sugar, and 150 of raisins. A loaf of raisin bread requires 1 unit of flour, 1 of sugar, and 2 of raisins, while a raisin cake needs 5, 2, and 1 units, respectively. a. If raisin bread sells for \$1.75 a loaf and raisin cake for \$4.00 each, how many of each should be baked so that gross i

### 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