Linear Programming formulation problem

In summary: 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 ----> minS.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)The constraints might be too restrictive. For example, the objective function might not be able to maximize profits if the number of table tops is
  • #1
Emilov
3
0
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 :)
 
Mathematics news on Phys.org
  • #2
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?
 
  • #3
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
 
  • #4
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?
 
  • #5
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
 

FAQ: Linear Programming formulation problem

1. What is linear programming formulation problem?

Linear programming formulation problem is a mathematical optimization technique used to find the best possible solution to a problem with linear constraints. It involves identifying the objective function and constraints in a linear equation format, and finding the optimal values for the decision variables that satisfy all the constraints.

2. What are the applications of linear programming formulation problem?

Linear programming formulation problem has a wide range of applications in various fields such as economics, management, engineering, and finance. It is commonly used to solve problems related to resource allocation, production planning, transportation, and investment portfolio optimization.

3. How is a linear programming problem formulated?

A linear programming problem is formulated by first identifying the decision variables, the objective function, and the constraints. The objective function represents the goal of the problem, and the constraints represent the limitations or restrictions. The problem is then solved using mathematical techniques such as the simplex method or the graphical method to find the optimal values for the decision variables.

4. What is the difference between linear and nonlinear programming?

The main difference between linear and nonlinear programming is the type of functions used in the objective function and constraints. In linear programming, all the functions are linear, meaning they have a constant slope, while in nonlinear programming, at least one function is nonlinear, meaning it has a varying slope. This makes nonlinear programming problems more complex and difficult to solve.

5. Can linear programming formulation problem handle real-life situations?

Yes, linear programming formulation problem can handle real-life situations as long as the problem can be represented using linear functions. It is a widely used optimization technique in various industries, and with advancements in technology, it is now possible to solve complex linear programming problems with multiple decision variables and constraints.

Similar threads

Replies
44
Views
4K
Replies
1
Views
1K
Replies
1
Views
1K
Replies
3
Views
1K
Replies
1
Views
1K
Replies
2
Views
3K
Replies
1
Views
2K
Back
Top