Linear Programming formulation problem

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Discussion Overview

The discussion revolves around formulating two linear programming (LP) models based on provided scenarios involving production constraints, resource availability, and cost minimization. Participants seek assistance in structuring these models, focusing on decision variables, constraints, and objective functions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • One participant presents a scenario involving a Finnish company producing three products (A, B, C) with constraints on raw materials and production capacity, seeking to maximize profit.
  • Another scenario involves a company producing tables, with constraints on production times, inventory, and demand over five years, aiming to minimize costs.
  • Participants discuss the need to identify decision variables, constraints, and the objective function for the LP models.
  • One participant expresses difficulty with the objective function in the second example and shares their current formulation, which includes overtime and inventory holding costs.
  • Another participant requests clarification on the progress made and thoughts on the formulation process.

Areas of Agreement / Disagreement

There is no consensus on the formulation details, as participants express varying levels of understanding and progress, particularly regarding the objective function in the second example.

Contextual Notes

Participants have not fully resolved the mathematical steps involved in formulating the LP models, and there are uncertainties regarding the correct setup of the objective functions and constraints.

Emilov
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Hello evryone :)
Is there someone who can help mi in formulating two LP models (Thinking) ?

Example 1

The Finnish company Suomi Oy produces three products A, B and C. For this, 2 types
of raw materials are used (I and II ). There are 5000 units of I and 7500 units of II
available. See the following table for the raw material requirements per unit:
Raw material requirements:
A B C
I 3 4 5
II 5 3 5

The time needed for each unit of product A is twice that of product B and three times
that of product C. The entire personnel of the company can produce the equivalent of
3000 units. The minimum demand of the three products is 600, 650 and 500 units,
respectively. The ratios of the number of units produced must be equal to 2 : 3 : 4.
Assume the pro ts per unit of A, B and C as 50, 50 and 80, respectively. Formulate the
problem as LP model in order to determine the number of units of each product that
will maximize the profit.Example 2

Home ltd. produces tables. A table consists of 2 table legs and 1 tabletop. The following
table gives the expected demand for tables in the next 5 years:

Demand: Year 1 Year 2 Year 3 Year 4 Year 5
Tables: 250 200 210 235 200

The next table gives the production times required by each product. There are 2 working
stations that have to be passed. Regular capacity can be increased by overtime. The
maximum overtime is 250 time units per working station and year. One hour overtime
costs 25 monetary units.

Working station 1 Working station 2
Table legs 2 3
Table tops 4 -
Tables - 4
Regular capacity 1500/year 2200/yearInventory holding costs (per unit) are 2 for tabletops, 5 for table legs and 10 for tables.
Initially there are 15 table tops, 14 table legs and 50 tables on stock. Inventory capacity
is 90m3. Table legs, table tops, and tables require 0:5m3, 1m3m, and 2m3m of inventory
space, respectively. Formulate a cost minimizing LP model.Thanks a lot to anyone in advance :)
 
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Emilov said:
Hello evryone :)
Is there someone who can help mi in formulating two LP models (Thinking) ?

Example 1

The Finnish company Suomi Oy produces three products A, B and C. For this, 2 types
of raw materials are used (I and II ). There are 5000 units of I and 7500 units of II
available. See the following table for the raw material requirements per unit:
Raw material requirements:
A B C
I 3 4 5
II 5 3 5

The time needed for each unit of product A is twice that of product B and three times
that of product C. The entire personnel of the company can produce the equivalent of
3000 units. The minimum demand of the three products is 600, 650 and 500 units,
respectively. The ratios of the number of units produced must be equal to 2 : 3 : 4.
Assume the pro ts per unit of A, B and C as 50, 50 and 80, respectively. Formulate the
problem as LP model in order to determine the number of units of each product that
will maximize the profit.

Welcome to MHB, Emilov! :)

Setting up an LP problem consists of the following steps.

Can you say what the decision variables are?
What are the constraints?
And the objective function?
 
I have done the first exercise, but I am still experiencing Problems with the LP formulation of the second one (generally with the objective function)... Please if anyone can help it would be very helpful. Thanks in advance
 
Emilov said:
I have done the first exercise, but I am still experiencing Problems with the LP formulation of the second one (generally with the objective function)... Please if anyone can help it would be very helpful. Thanks in advance

How far did you get?
Any thoughts?
 
I like Serena said:
How far did you get?
Any thoughts?

Hi. I think I am experiencing problems with the Objective function. Up to now I have done the LP this way:
Obj. Func: the sum of overtime costs + the sum of inventory holding costs ----> min

S.t:
2x + 4y <=250 (overtime of machine one)
3x + 4z <=250 (overtime of machine 2)
5x+4y+4z<=500 (overtime both machines)
0.5x+ y + 2z <=90 (max capacity of inventory)

This is my thoughts... Please if can help until 1 o'clock because I have to hand in the homework than. Thanks
 

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