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Linear Programming

A company needs to lease warehouse storage space

A company needs to lease warehouse storage space for five months at the start of the year. The space requirements (in square feet) and the leasing costs of each type of lease are given in the two tables below: Month Required Space (sq. feet) Jan 15,000 Feb 10,000 Mar 20,000 Apr 5,000 May 25,000 Lease Term (months) Co

Create and solve a linear program which maximizes Sunco's daily profits. What are the optimum decisions, i.e. the barrels of crude oil used to create the gasoline and the advertising dollars spent on stimulating the demand for gasoline?

Sunco Oil Co. manufactures three types of gasoline: Gas 1, Gas 2 and Gas 3. Each type is produced by blending three type of crude oil: Crude 1, Crude 2 and Crude 3. The sales price per barrel of gasoline and the purchase price per barrel of crude oil is given in the following table: Gasoline Type Gas Selling Price Per Barrel C

Linear Programming : Using the Simplex Method to Minimize C

In this problem I am trying to get rid of the artificial variable using the two phase method. However all of the rows either have negatives or zeros and my final answer keeps coming out to be a negative and none of the other answers plug into the constraints. The problem is Using Simplex method minimize C:

Linear Programming : Formulating Equations and Minimizing Cost

A biologist must make a nutrient for her algae. The nutrient must contain three basic elements D, E, F, and must contain at least 10kg of D, 12kg of E, and 20Kg of F. The nutrient is made from three ingredients, I, II, III. The quantity of D, E, F in one unit of each of the ingredients is given in the following chart.

Linear Programming : Scaling, Unbounded LPs and Feasible Region

Question #1 A company produces three products. The per-unit profit, labor usage, and pollution produced per unit are given in the table 1. At most, 3 million labor hours can be used to produce the three products, and government regulations require that the company produce at most 2 lb of pollution. If we let Xi = units produ

Justify Linear Programming Statements : Equality Constraints

For each statement, state whether it is true or false. Be sure to justify your answer. a) Suppose you are given a linear program in Rn with mE equality constraints and mI inequality constraints. Let x be an element of the polyhedron at which n - mE inequality constraints are active. Then x must be an extreme point of the poly

Proof in Linear Programming - Extreme Point

Can anyone help me to prove this? I'm really stuck with geometry in Linear Programming... (See attached file for full problem description and equations) --- Assume P is a polyhedron and H is a supporting hyperplane to P. Prove that is an extreme point of if and only if is an extreme point of P.

Linear programming

Find the complete optimal solution to this linear programming problem. Min 3X + 3Y s.t. 12X + 4Y > 48 10X + 5Y > 50 4X + 8Y > 32 X , Y > 0

Proof in Linear programming

Please help me to find out how I can do this (See attached file for full problem description) --- Let (see attachment) It is clear that we can rewrite (attached) as (attached) , i.e. as a system of linear inequalities. (I've done this). Show that in fact we can rewrite (attached) as a system of (attached) linear i

Linear Programming (5 Problems)

Question 1 Cully furniture buys 2 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 1800

Linear programming

(See attached file for full problem description) --- Indicate whether the sentence or statement is true or false. _____ 1. Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem. _____ 2. When using linear program

Maximizing or Minimizing and Application to Linear Programming

(See attached file for full problem description) --- 1) Discuss from your own experience a case where you had to maximize or minimize something and also how you think linear programming techniques might have helped you arrive at your final decision. 2) Read the short, well-written article on the Simplex Method which

Quantitative Methods

Homework problems. File is attached. --- True/False Indicate whether the sentence or statement is true or false. ______ 1. A linear programming model consists of decision variables, constraints, but no objective function. ______ 2. Linear programming models exhibit linearity among all constraint relationships and th

Linear Programming Question

The particular solution corresponding to the simplex tableau x y u v M 0 -3 1 1 0 2 1 2 0 0 0 6 0 -4 0 5 1 10 is: a. X=2, y=6, u=10, v=0, M=0 b. X=2, y=6, u=0, v=0, M=0 c. X=6, y=0, u=0, v=0, M=10 d. X=6, y=o, u=6, v=0, M=10 e. None of the above

Linear Programming and Simplex Methods : Objective Function

New cars are transported from docks in Baltimore and New York to dealerships in Pittsburgh and Philadelphia. The dealership in Pittsburgh needs 20 cars and the delaership in Philadelphia needs 15 cars. It costs $60 to transport a car from Baltimore to Pittsburgh, $45 to transport a car from Baltimore to Philadelphia, $65 to tr

Linear Programming and Simplex Methods : Minimization

The linear programming problem. Minimize 5x - y subject to: -2x - 2y < 12 -3x + 2y > 0 x > 0, y > 0 is equivalent to the linear programming problem: a. Maximize 5x - y subject to: -2x -2y < 12 3x - 2y < 0 x > 0, y > 0 b. Maximize 5x-y subject to: -2x -2y < 12 -3x + 2y > 0 x >

Linear Programming and the Simplex methods : Surpluses

Consider the following linear programming problem: A workshop of Peter's Potters makes vases and pitchers. Profit on a vase is $3.00; profit on a pitcher is $4.00. Each vase requires ½ hour of labor, each pitcher requires 1 hour of labor. Each item requires 1 unit of time in the kiln. Labor is limited to 4 hours per day a

Linear Programming : Writing Constraints and Maximizing Profit

The Chop is the manufacturer of the store brand of hatchets and axes sold by various home hardware supply stores. Each item consists of a hickory handle produced in the local processing facility and a steel blade forged and polished in the local machine shop. These two items are then transported to an assembly area where the b

Linear Programming with Excel

Acme estimates it costs $1.50 per month for each unit of this appliance carried in inventory (estimated by averaging the beginning and ending inventory levels each month). Currently, Acme has 120 units in inventory on hand for the product. To maintain a level workforce, the company wants to produce at least 400 units per month.

Network Model Transportation Problem: Supply and Demand

Please help with the following problem. Canning Transport is to move goods from three factories to three distribution centers. Information about the move is given below. Give the network model and the linear programming model for this problem. Supply at Source Demand at Destination 200 A

Linear Programming of Transportation and Shipment Problem

I need some help with a network diagram and formulation of the linear programming model. A company ships computers from factories to stores per week as follows: Factory #1 produces 400 computers per week. Factory #2 produces 200 computers per week. Factory #3 produces 150 computers per week. Store #1 needs 200 computers

Linear Programming : Simplex Method in Tableau Form

The following problem is something that needs to be put into tableau iterations, but I'm not sure of my answers on it... I'm catching on slowly, but would like to have something to use to check my work... This is a homework problem, but the homework is graded on participation, not correctness in this distance learning class.

Maximum-Minimum Theorem : Continuity and Bounded Functions

(d) Does the conclusion of the Maximum-Minimum Theorem always hold for a bounded function f : R --> R that is continuous on R? Prove or give a counterexample. (a) Fix a, b E R, a < b. Prove that if f [a, b] -->R is continuous on [a, b] and f(x)&#8800;0 for all x E [a, b], then 1/f(x) is bounded on [a, b]. (b) Find a, b E R, a