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## #1 2023-02-04 01:44:40

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

### Help me Please solve this ques ASAP

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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## #2 2023-02-04 03:33:26

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

### Re: Help me Please solve this ques ASAP

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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## #3 2023-02-04 21:28:02

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

### Re: Help me Please solve this ques ASAP

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.