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**Harsh22****Novice**- Registered: 2023-02-04
- Posts: 2

Use the simplex method to solve the following LPP

Maximize Z = 20?1 + 10?2 + ?3

Subject to

3?1 − 3?2 + 5?3 ≤ 50

?1 + ?3 ≤ 10

?1 − ?2 + 4?3 ≤ 20

?1, ?2, ?3 ≥ 0.

Does the LPP has an optimal solution? If so, find it else, explain why not?

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 41,293

Hi Harsh22,

LPP:

*It is an optimization method applicable for the solution of

optimization problem where objective function and the constraints

are linear.

*It was first applied in 1930 by economist, mainly in solving resource

allocation problem During World War II, the US Air force sought

more effective procedure for allocation of resources George B.

Dantzig, a member of the US Air Force formulate general linear

problem for solving the resources allocation problem.

“A Linear Programming Problem is one that is concerned with finding the

optimal value (maximum or minimum value) of a linear function (called

objective function) of several variables (say x and y), subject to the conditions

that the variables are non-negative and satisfy a set of linear inequalities

(called linear constraints). The term linear implies that all the mathematical

relations used in the problem are linear relations while the term

programming refers to the method of determining a particular programme or plan of action."

Hope this helps.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,633

hi Harsh22

Welcome to the forum.

Sorry but this problem makes no sense as entered. It has lots of '?' where it needs variables such as x, y, and z before it becomes an LPP.

A typical 3D constraint should look like this:

ax + by + cz < N where a, b, c, and N are numbers and < might alternatively be > etc

3?1 − 3?2 + 5?3

isn't a constraint. Did you type something else and it's been displayed differently here on the forum. Ordinary text should allow you do show this.

Once there are a set of constraints these bound a solution space and the best values of x, y, and z can be determined.

Please post again, clarifying this.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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