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Linear Programming

Quantitative Stats

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

Quantitative Methods Linear/Integer Programming Study Questions

_______ 1. Linear programming models have decision variables for measuring the level of activity. _______ 2. In a transportation problem, a demand constraint for a specific destination represents the amount of product demanded by a given destination (customer, retail outlet, store). _______ 3. In a problem involving c

Quantitative Methods (Linear Programming Model) : Optimizing a Teaching Schedule

The Department of Management Science and Information Technology at Tech The management science and information technology department at tech offers between 36 and 40 three-hour course sections each semester. Some of the courses are taught by graduate student instructors, whereas 20 of the course sections are taught by the 10

Linear Programming - optimal solution

Max Z = 3x1 + 5x2 s.t. 7x1 + 12x2 <= 136 3x1 + 5x2 <= 36 x1, x2 >=0 and interger Find the optimal solution put your answer int he form of a solution for Z= enter xx only

Multiple choice questions

Find the complete optimal solution to this linear programming problem. Min 5X + 6Y s.t. 3X + Y >= 15 X + 2Y >= 12 3X + 2Y >= 24 X,Y >=0 x=3,y=3,z=48,s1=6,s2=0,s3=0 x=6,y=3,z=48,s1=6,s2=0,s3=0 x=3,y=6,z=48,s1=3,s2=0,s3=0 x=6,y=3,z=52,s1=6,s2=0,s3=0 I think the correct answer is x=3,y=6,

Non-Linear Programming using Excel Solver Add-in

Problem: A company makes products C and D from 2 resources, labor and material. The company wants to determine the selling price which will maximize profits. One unit of C costs $30 to make and demand is estimated to be 50 - .09 * Price of C. One unit of D costs $20 to make and demand is estimated to be 30 - .14 * Price of

Optimal solutions in linear programming

Explain the following statement with an example: the optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem. Do you agree with the following two questions? 1. Why should the optimal solution of any Linear Programming solution be lying at the corner points of t

Linear Programming : Maximizing Profit; Interest and Principle Problem

1. A company makes three products, A, B, and C. There are 500 pounds of raw material available. Each unit of product A requires 2 pounds of raw material, each unit of product B requires 2 pounds of raw material, and each unit of product C requires 3 pounds. The assembly line has 1,000 hours of operation available. Each unit

Transportation and Transshipment Problems : Constraints, Supply and Demand

1. In setting up the an intermediate (transshipment) node constraint, assume that there are three sources, two intermediate nodes, and two destinations, and travel is possible between all sources and the intermediate nodes and between all intermediate nodes and all destinations for a given transshipment problem. In addition, ass

Linear Programming : Solving by a Graphical Method

Let x be the number short-answer questions and y be the number of essay quesitons. Given : 9 points for short - answer 25 points for essay. x <=10, obviously x >=9 y<=10, obviously y >=3 x + y <=19 ( constraints) Maximum score Maximum Z= 9x + 25 y Subject to the constraints, x+y<=19, x>=9

Linear Programming : Finding Constraints and Solving Word Problems

Stan and Ron's hobby is building birdhouses. The number of wren houses cannot exceed 2 times the number of martin houses. They cannot make more than 60 wren houses or more than 70 martin houses. The total production cannot exceed 90. The profit on a wren house is $9.30 and the profit on a martin house is $5.50. Find the maximum

Using LINDO to Solve a Linear Programming Problem

I want to know how to use Lindo to solve an example in my textbook. Please need detail instructions so I can feel comfortable using LINDO to solving larger problems, The example in the text uses excel spreadsheet, but I want to know how to use LINDO without excel. How do I write out the objective function, supply and demand c

Big-M method

Consider the following algorithm for solving a linear program in standard form without having to use the Big-M method: Choose any basis. Check to see if this basis is primal feasible. If so, use this as your initial BFS and solve the problem with simplex. If the basis is primal infeasible, solve the problem using dual si

Proof Optimal Solution

Consider a symmetric square matrix A and the following linear program: Min cx St Ax > c x > 0 Prove that if x* satisfies Ax* = c and x* > 0 then x* is an optimal solution to this linear program.

Reliabilty Theory Questions

These questions are a part of a Operations Research class with a section on Reliability Theory. (See attached file for full problem description with proper symbols and equations) --- Question Let N be a non-negative, integer-valued random variable, Show that P{N > 0} >= (E[N])2

Linear Programming : Formulate Decision and Solve by Computer

9-1 Horrible Harry's Horrible Harry's is a chain of 47 self service gas stations served by a small refinery and mixing plant. Each day's product requirements are met by blending feedstocks on hand at midnight. The volumes vary daily, depending on the previous day's refinery output and on bulk receipts. The entire operatio

Dual Simplex Method and Primal Simplex Method

Exercise 4.25 This exercise shows that if we bring the dual problem into standard form and then apply the primal simplex method, the resulting algorithm is not identical to the dual simplex method. Consider the following standard form problem and its dual. minimize x1 + x2 maximize p

Formulate a Linear Programming model

5. Bob Brown's 40th birthday party promised to be the social event of the year in Illinois. To prepare, Bob stocked up on the following liquors. Liquor On Hand (ounces) Bourbon 52 Brandy 38 Vodka 64 Dry Vermouth 24 Sweet Vermouth 36 Bob decided to mix four drinks for the party: Chaunceys, Sweet Italians, Bourbon on th

Matrix Proofs : Linear Programming, Duality, Feasibility and Optimal Solutions

Exercise 4.26 Let A be a given matrix. Show that exactly one of the following alternatives must hold. (a) There exists some x does not equal 0 such that Ax = 0, x > 0. (b) There exists some p such that p'A> 0'. Exercise 4.27 Let A be a given matrix. Show that the following two statements are equivalent. (a) Every vector such

Linear Programming : Proof using Duality and the Farkas Lemma

This question is from linear programming. I want to use duality (it's so obvious), farkas lemma (alternative solution) and all. (See attached file for full problem description with equations) --- (a) Let . Prove that one of the following systems has a solution but not both: (b) Prove or disprove the following cla

Linear Programming : Finding the Optimal Value by a Graphical Method

1. AA Auto manufactures luxury cars and trucks. The company believes that its most likely customers are high-income women and men. To reach these groups, AA Auto has embarked on an ambitious TV advertising campaign and has decided to purchase 1-minute commercial spots on two types of programs: comedy shows and football games.