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Linear Programming

Quantitative Methods : Linear Programming

1. For the linear program: Max 4A + 1B s.t. 10A + 2B < 30 3A + 2B < 12 2A + 2B < 10 A, B > 0 a. write this in standard form. b. solve the problem using the graphic solutions procedure. c. what are the values of the three slack variables at the optimal solutions? 2. Consider the follwoing linear program: Min 2A

Quantitative Methods - Linear Program Graphic Solution Procedure

1. For the linear program: Max 2A + 3B s.t. 1A + 2B < 6 5A + 3B < 15 A,B > 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. Max 5A + 5B s.t. 1A <

Linear Programming Models with Constraints

1. Which of the following mathematical relationships could be found in a linear programming model? And which could not (why)? a. -1A + 2B < 70 b. 2A - 2B = 50 c. 1A - 2B2 < 10 d. 3 squareroot A + 2B > 15 e. 1A + 1B = 6 f. 2A + 5B + 1AB < 25 2. Find the solutions that satisfy the following const

Vector Space Axioms, Zero Element and Geometric Method of Linear Programming

Please see the attached file for the fully formatted problems. 1) Let R+={x/0<x} (that is, the set of positive real numbers). Define the operation of addition on this set by x+y=xy. Show that with this definition there is a zero element, and that every x in R+ has an inverse. Determine what the zero element is, and for any gi

Linear Programming - Staffing

How would you define in linear programming format that an employee has to work 5 consecutive days, and then has 2 days off?

Subsets, Projection Maps, Basis and Direct Sums

Let n >= 1. Define the subsets U and W in V = F^n as follows: U = {(x_1, . . . , x_n) : x_1 + . . . + x_n = 0} W = {(x_1, . . . , x_n) : x_1 = . . . = x_n} a) Prove that U and V are subspaces of V . b) Prove that V = is the "direct sum" of U and W. c) Let (v_1, . . . v_n) = ((1, 0, . . . , 0), (0, 1, . . . , 0), . . . ,

Linear programming

I'm not sure how to go about finding the optimal solution for part a and b ( please see the attached file it includes my partial solution to the question)

Quantitative Methods - Tom's Inc.

Tom's Inc., produces various Mexican food products and sells them to Whole Foods, a chain of grocery stores located in the United States. Tom's Inc. makes two salsa products: Whole Foods Salsa and Mexico City Salsa. The two products have different blends of whole tomatoes, tomato sauce, and tomato paste. The Whole Foods Salsa

Constraints: The LP problem whose output follows determines how many necklaces, bracelets, rings, and earrings a jewelry store should stock. The objective function measures profit; it is assumed that every piece stocked will be sold.

The LP problem whose output follows determines how many necklaces, bracelets, rings, and earrings a jewelry store should stock. The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes.

Linear Programming Objective Function

Which of the following could be a linear programming objective function? Z = 1A + 2B / C + 3D Z = 1A + 2BC + 3D Z = 1A + 2B + 3C + 4D Z = 1A + 2B2 + 3D all of the above.

Slope of Objective Function

In a linear programming problem, the binding constraints for the optimal solution are 5X + 3Y < 30 2X + 5Y < 20. Fill in the blanks in the following sentence: As long as the slope of the objective function stays between _______ and _______, the curren

Linear Programming

The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1

Linear programming

The linear programming problem whose output follows is used to determine how many bottles of fire red nail polish (x1), bright red nail polish (x2), basil green nail polish (x3), and basic pink nail polish (x4) a beauty salon should stock. The objective function measures profit; it is assumed that every piece stocked will be sol

Linear programming

The linear programming problem whose output follows is used to determine how many bottles of fire red nail polish (x1), bright red nail polish (x2), basic green nail polish (x3), and basic pink nail polish (x4) a beauty salon should stock. The objective function measures profit; it is assumed that every piece stocked will be so

Linear Programming: Finding Maximum Profit

Question: Cully furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 c

Linear Programming Model Destination

Destination Source Business Education Parsons Hall Holmstedt Hall Supply BakerHall 10 9 5 2 35 Tirey Hall 12 11 1 6 10 Arena 15 14 7 6 20 Demand 12 20 10 10 1a. If you were going to write this as a linear programming model, how many decision variables would there be, and how many constraints would there be? 1b.

Linear Programming Model

Golf Shafts Inc (GSI) produces graphite shafts for several manufacturers of golf clubs. Two GSI manufacturing facilities one located in San Diego and the other in Tampa, have the capability to produce shafts in varying degrees of stiffness ranging from regular models used primarily by average golfers. GSI just received a contrac

Quantum

See attached file for full problem description. 13. Diet Mix Problem 1 The dietician for the local hospital is trying to control the calorie intake of the heart surgery patients. Tonight's dinner menu could consist of the following food items: chicken, lasagna, pudding, salad, mashed potatoes and jello. The calories per s

Feasible or not feasible solutions

1. Linear Programming Properties Which of the following statements is not true? a) An infeasible solution violates all constraints. b) A feasible solution point does not have to lie on the boundary of the feasible solution. c) A feasible solution satisfies all constraints. d) An optimal solution satisfies all constraints

Linear Programming Models

Steelco manufactures two types of steel at three different steel mills. During a given month, each steel mill has 200 hours of blast furnace time available. Because of the differences in the furnaces at each mill, the time and cost to produce a ton of steel differ for each mill, as listed in the file P04_62.xls. Each month Steel

Quantitative Analysis - 50 Multiple choice Questions

1. Which of the following is not a reason for the failure of a particular Quantitative analysis technique in solving a problem? a. underestimating the total cost of using quantitative techniques b. failure to define the real problem c. under-emphasis on theory and over-emphasis on application d. underestimating the total

Linear Programming : Maximizing Profit using Matrix Methods

Matrices have a number of interesting mathematical attributes, such as their dimensions, how they can be derived from linear systems, and the kinds of operations that can be performed on them. Copy the questions to a Microsoft Word document and use an equation editor to enter the answers. Please answer the following question