SUNY Plattsburgh Artificial Variables Linear Programming Task

Description

1 attachmentsSlide 1 of 1attachment_1attachment_1

Unformatted Attachment Preview

1. Use the Simplex Method to solve the following LP:
max 𝑍 = π‘₯1 + 2π‘₯2 + 4π‘₯3
subject to
3π‘₯1 + π‘₯2 + 5π‘₯3 ≀ 10
π‘₯1 + 4π‘₯2 + π‘₯3 ≀ 8
2π‘₯1
+ 2π‘₯3 ≀ 7
π‘₯1 , π‘₯2 , π‘₯3 β‰₯ 0
2. Solve the following LP using the Two-phase method:
max 𝑍 = 2π‘₯1 + 3π‘₯2
subject to
π‘₯1 + 2π‘₯2 ≀ 4
π‘₯1 + π‘₯2 = 3
π‘₯1 , π‘₯2 β‰₯ 0
3. Solve the following LP using the Two-phase method:
max 𝑍 = 3π‘₯1 + 2π‘₯2 + 4π‘₯3
subject to
2π‘₯1 + π‘₯2 + 3π‘₯3 = 60
3π‘₯1 + 3π‘₯2 + 5π‘₯3 β‰₯ 120
π‘₯1 , π‘₯2 , π‘₯3 β‰₯ 0
4. The Philbrick Company has two plants on opposite sides of the United States. Each
of these plants produces the same two products and then sells them to wholesalers
within its half of the country. The orders from wholesalers have already been received
for the next 2 months (February and March), where the number of units requested are
shown below. (The company is not obligated to completely fill these orders but will do
so if it can without decreasing its profits.)
Each plant has 20 production days available in February and 23 production days
available in March to produce and ship these products. Inventories are depleted at the
end of January, but each plant has enough inventory capacity to hold 1,000 units total
of the two products if an excess amount is produced in February for sale in March. In
either plant, the cost of holding inventory in this way is $3 per unit of product 1 and $4
per unit of product 2.
Each plant has the same two production processes, each of which can be used to
produce either of the two products. The production cost per unit produced of each
product is shown below for each process in each plant.
The production rate for each product (number of units produced per day devoted to that
product) also is given for each process in each plant below.
The net sales revenue (selling price minus normal shipping costs) the company receives
when a plant sells the products to its own customers (the wholesalers in its half of the
country) is $83 per unit of product 1 and $112 per unit of product 2. However, it also
is possible (and occasionally desirable) for a plant to make a shipment to the other half
of the country to help fill the sales of the other plant. When this happens, an extra
shipping cost of $9 per unit of product 1 and $7 per unit of product 2 is incurred.
Management now needs to determine how much of each product should be produced
by each production process in each plant during each month, as well as how much each
plant should sell of each product in each month and how much each plant should ship
of each product in each month to the other plant’s customers. The objective is to
determine which feasible plan would maximize the total profit (total net sales revenue
minus the sum of the production costs, inventory costs, and extra shipping costs).
a. Formulate a complete linear programming model in algebraic form that shows
the individual constraints and decision variables for this problem.
b. Formulate this same model on an Excel spreadsheet instead. Then use the Excel
Solver to solve the model.
c. Formulate this same model in python then use cplex solver to solve it.

Purchase answer to see full
attachment

Tags:
Parameters

decision variables

Row operations

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.

Reviews, comments, and love from our customers and community:

Article Writing

Keep doing what you do, I am really impressed by the work done.

Alexender

Researcher

PowerPoint Presentation

I am speechless…WoW! Thank you so much!

Stacy V.

Part-time student

Dissertation & Thesis

This was a very well-written paper. Great work fast.

M.H.H. Tony

Student

Annotated Bibliography

I love working with this company. You always go above and beyond and exceed my expectations every time.

Francisca N.

Student

Book Report / Review

I received my order wayyyyyyy sooner than I expected. Couldn’t ask for more.

Mary J.

Student

Essay (Any Type)

On time, perfect paper

Prof. Kate (Ph.D)

Student

Case Study

Awesome! Great papers, and early!

Kaylin Green

Student

Proofreading & Editing

Thank you Dr. Rebecca for editing my essays! She completed my task literally in 3 hours. For sure will work with her again, she is great and follows all instructions

Rebecca L.

Researcher

Critical Thinking / Review

Extremely thorough summary, understanding and examples found for social science readings, with edits made as needed and on time. Transparent

Arnold W.

Customer

Coursework

Perfect!

Joshua W.

Student

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>