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Linear Programming

Simplex Algorithm Problem

6. Consider the problem maximise 2x_1 + 3x_2 + x_3 subject to x_1 + 2x_2 + 3x_3 + x_4 = 6 2x_1 + x_2 + 2x_3 + x+5 = 4 x_1, ..., x_5 >= 0 with initial tableau: 1 2 3 1 0 | 6 2 1 2 0 1 | 4 ------------- 2 3 1 0 0 | 0 and final tableau: . . . 2/3 -(1/3) | . . . . -(1/3) 2/3 | . --------------------- . . . -(

Linear Programming

A small shop located in Utica sells a variety of dried fruits and nuts. The shop caters to travelers of all types; it sells one-pound boxes of individual items, such as dried bananas, as well as two kinds of one-pound boxes of mixed fruits and nuts, called "Trail Mix" and "Subway Mix". Because of the health inspection issues,

Managerial Business

A farmer's family is making plans for the year's planting. Its members are considering planting corn, tomatoes, potatoes, and strawberries. They have 50 acres to plant on. The aim is to determine what it costs to plant an acre of each crop, computing the yield in bushels, forecasting the revenue for a bushel of each crop, and ch

Linear Problem Model Question

A production manager is faced with the question of how to allocate the manufacturing of a microwave oven between his own company and a subcontractor, because neither firm can handle the demand alone. Fabrication costs are $10 per unit within the company and $20 per unit from the subcontractor; assembly costs are $8 per unit

Solver application for linear programming

Problem 8-4. (Animal feed mix problem) The Battery Park Stable feeds and houses the horses used to pull tourist-filled carriages through the streets of Charleston's historic waterfront area. The stable owner, an ex-racehorse trainer, recognizes the need to set a nutritional diet for the horses in his care. At the same time, he w

Linear Programming Model: Example Problem

A company wants to offer their employees a three-day training program on team building and a two-day program on problem solving. They have requested at least 8 training sessions on team building and at least 10 training sessions on problem solving. Furthermore, the total number of training sessions offered must be 25. The tra

Controlling Inventory

Lila Battle has determined that the annual demand for number 6 screws is 100,000 screws. Lila, who works in her brother's hardware store, is in charge of purchasing. She estimates that it costs $10 every time an order is placed. This cost includes her wages, the cost of the forms used in placing the order, and so on. Furthermor

Linear programming in an Excel Solver

Need tutorial assistance involving Excel Solver. The city of Spring View is taking bids from six bus companies on the eight routes that must be driven in the surround school district. Each company enters a bid on how much it will charge to drive selected routes, although not all companies bit on all routes. The data are conta

Solving a Problem in Linear Programming

Min 2A + 2B s.t. 1A + 2B is less than or equal to 12 3A + 1B is greater than or equal to 13 1A - 1B = 3 A,B is greater than or equal to 0 a. Show the feasible region. b. What are the extreme points of the feasible region? c. Find the optimal solution using the graphical solution procedure.

Using a Graph to Solve Linear Programming

Min A + 2b s.t. A + 4b is less than or equal to 21 2A + B is greater than or equal 7 3A + 1.5B is less than or equal to 21 -2A + 6B is greater than or equal to 0 A,B is greater than or equal to 0 A. Determine the amount of slack or surplus for each constraint?

Use exponential smoothing.

The following table lists the worldwide shipments of personal computers (in thousands) according to Dataquest. Year Shipments (in thousands) 1990 23,738 1991 26,966 1992 32,411 1993 38,851 1994 47,894 1995 60,171 1996 71,065 1997 82,400 1998 97,321 (a) Use exponential smoothing to determine the forecast of shipment

Linear Programming for Optimal Solutions and Functions

Consider the following linear programming problem: Min A + 2B s.t. A +4B is less than or equal to 21 2A+B is greater than or equal to 7 3A+1.5B is less than or equal to 21 -2A + 6B is greater than or equal to 0 A,B is greater than or equal to 0 1. Find the optimal solution using the graphical solut

Non-linear scalar equation(Matlab only)

All the roots of the scalar equation x-4sin(2x)-3=0, are to be determined with at least 10 accurate digits, (n accurate digits is equivalent to a relative error smaller than 0.5 x 10^-n) 1) Using Matlab, plot f(x)=x-4sin(2x)-3. All the zero crossings should be in the plot. How many are there? 2) Write a program

Linear Programming: Inequalities

Question 2 A linear programming problem may have more than one set of solutions. Answer True False Question 3 In minimization LP problems the feasible region is always below the resource constraints. Answer True False Question 19 Consider the following minimization problem: Min z = x1 + 2x2 s.t.

Linear Program for Optimal Solutions

Given the linear Program: Max 3A+4B s.t. -1A+2B is less than or equal to 8 1A+2B is less than or equal to 12 2A+1B is less than or equal to 16 A,B is greater than or equal to 0 A. Show the feasible region? b. Find the optimal solution using the graphical solution procedure?

optimum solutions in a linear programming

2. A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Each product requires 10 hours of processing time on line 1, while on line 2 products 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is

Minimum sum of abssolute values & Min max of abssolute values

Hi, I need help with the following problem linear programming question that asks for two linear programming solutions for a timer series that Min sum of abs values & Min max of abs values. I have attached the detailed questions in the attached Word document. I have already solved question 1, which is attached in an Excel f

Use LP relaxation to solve Mix Integer programming problem

Consider the following all-integer linear program: Max 2x1+3x2 s.t. 4x1+9x2<36 7x1+5x2<35 1x1+2x2<10 X1,x2>0 and x1 integer a. Graph the constraints for this problem. Indicate on your graph all feasible mixed-integer solutions. b. Find the optimal solution to the LP Relaxation. Round the value of x1 down

Develop LP Relaxation.

Please help with the following problem. Indicate which of the following is an all-integer linear program and which is mixed-integer linear program. Write the LP Relaxation for the problem but do not attempt to solve a. Max 30x1 + 25x2 s.t. 3x1+1.5x2<400 1.5x1+2x2<250 1x1+1x2<150 X1,x2>0and x2 integer b. Min 3

Finite maths, linear programming

write the basic solution for tte simplex tableau determined by setting the nonbasic variables. (1) xi x2 x3 x4 x5 z 3 4 0 3 1 0 12 1 5 1 7 0 0 21 -3 4 0 1 0 1 18 (2) x1 x2 x3 x4 x5 z 2 0 3

Linear Programming

Missouri Mineral Products (MMP) purchases two unprocessed ores from Bolivia Mining, which it uses in the production of various compounds. Its current needs are for 800 pounds copper, 600 pounds of zinc, and 500 pounds of iron. The amount of each mineral found in each 100 pounds of the unprocessed ores and MMP's cost per 100 poun

Linear Programming Minimum Transport Costs

2) Describe the effect on the minimum transportation cost when capacity at each factory or warehouse is altered by adding or subtracting one ton. What are the minimum capacity changes at Glasgow that will alter the optimum set of routes and what will those alterations be? Explain how you arrive at each one of your answe

Using Simplex Method with Mixed Constraints

Using Simplex Method with Mixed Constraints, Maximize P=0.9x+y subject to 0.6x+0.4y &#8804; 2800 0.2y &#8804; 800 0.2x+0.2y &#8805; 1000 x,y &#8805; 0 where x = number of pounds of Senior Citizen's Feast cereal and y = number of pounds of Kids Go cereal and P(x,y) is the profit function based on

Calculating Optimal Inventory Parameters

Annual demand is 4000 units the cost is $90, the inventory carrying cost is 10% of each unit. The average ordering cost is $25. Demand per week is 80 What is the EOQ? What is the ROP? What is the average inventory, what is the annual holding cost? How many orders per year would be placed, what is the annual ordering cos

Classify inner products.

Determine which of the following are inner products in R^3.... x=(x_1, x_2, x_3), y=(y_1, y_2, y_3) a) <x,y>= x_1 y_1+x_3 y_3 b) <x,y>= x_1 y_1- x_2 y_2 + x_3 y_3 c) <x,y>= 2x_1 y_1 + x_2 y_2 + 4x_3 y_3 d) <x,y>= x^2_1 y^2_1 + x^2_2 y^2_2 + x^2_3 y^2_3

Optimal Portfolio allocation

A $1 million portfolio is currently invested in fund A. Fund A beta is 1.6. The portfolio manager considers switching some of the portfolio into fund B that has a beta of 0.6. a. What would be the new portfolio allocation (investment in A and in B) that will achieve a portfolio beta goal of 1.20?

Average Yearly Increased World's Population

In 1987, the world's population reached 5 billion people, and by 2012 the world's population is expected to reach 7 billion people. (Source: U.S. Census Bureau). (a) Find the average yearly increase in the world's population from 1987 to 2012. (b) Write a linear equation that estimates the world's population P in billions x

Linear Programming

The Pittsburg Chemical Company of Akron, Ohio, produces a variety of products within its four divisions for agricultural and industrial customers. Division II will produce only two products this week for sale to wholesale distributors and all production will be sold. Product 1 yields a contribution margin (contribution to prof

Linear programming model on excel is assessed.

The Bluegrass Distillery produces custom blended whiskey. A particular blend consists of rye and bourbon whiskey. The company has received an order for a minimum of 400 gallons of the custom blend. The customer specified that the order must contain at least 40% rye and not more than 250 gallons of bourbon. The customer also spec