Operations Research: TORA Tutorial for Reddy Mikks and Diet Problems

This assignment is a practical application of the TORA software in Operations Research, focusing on solving linear programming problems. The assignment begins with an introduction to the TORA software, explaining its functionalities and the types of problems it can address, including linear equations, the transportation model, integer programming, and queuing models. The core of the assignment involves two problem statements: the Reddy Mikks problem, a maximization problem, and a diet problem, a minimization problem. The solution outlines the step-by-step procedures to input data, solve the problems graphically, and interpret the results. For the Reddy Mikks problem, the assignment emphasizes the identification of feasible solutions and the maximization of total profit. For the diet problem, it focuses on minimizing the cost while meeting dietary constraints. The conclusion highlights the ease of solving problems using TORA, making it a helpful tool for operations research.

Lab # 02 1
Minimizing Diet and Maximizing Reddy Mikks CO. Problems
by using TORA
Introduction:
TORA tutorial software deals with the following algorithms:
 linear equations
 Linear programming
 Transportation model
 Integer programming
 Network models
 project analysis by CPM/PERT
 Poisson queuing models
 Zero-sum games
TORA is a free software database development and administration GUI, available under the GNU
General Public License. It features a PL/SQL debugger, an SQL worksheet with syntax highlighting, a
database browser and a comprehensive set of database administration tools
Objective:
To know about TORA and how to use it
Problem statement 1:
Procedure:
Procedure consist of following steps
(1) Double click on tora icon.
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Lab # 02 2
(2) Now clicking on ‘click here’.
(3) Now clicking on ‘linear programing’.
(4) Giving the numbers of digits before decimal ‘N’ and numbers of digits after decimals ‘D’. Then
clicking on ‘Go to input screen’.
(5) After giving the problem title ,no of variables and no of constraints .click ‘tab’ and give the data.
Now solving the problem of Reddy mix which is maximization problem:
(1) Follow all the above step
(2) Input the data to TORA i.e. problem statement, no of constraint, and no of variables. Then
press enter you will get the following window.
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Lab # 02 3
(3) Now click on the on the “solve menu” and save the file
(4) Click on “solve problem” and select the “graphical”
(5) Click on “go to output screen”
(6) Graphical solution is as follows.
Now doing minimization problem for diet:
Problem statement 2:
Procedure:
(1) Follow the same procedure as followed in problem 1
(2) Input data to TORA.
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Lab # 02 4
(3) Its graphical solution is as follow
Result and discussion:
Reddy mikks: Any value of x1 and x2 that satisfy all the constraint constitute a feasible solution
otherwise the solution will be infeasible. Substitute x1=3, x2=1 in the left hand side of each equation.
Constraint (1) 6x1+4x2=6*3+4*1=22 which is less than the right hand side (24). Constraint 2 through
5 will yield similar conclusion The goal of the problem is to find the feasible solution that maximizes
the total profit. The answer we see from the graphical solution.
Diet problem: here the constraint 2 and 3 passes through the origin. In the second constraint x1=200
will yield .21*200-.3x2=0, or x2=140this means that the straight line .21x1-.3x2=0 passes through the
(0,0) and (200,140). The (0,0) cannot be used as reference point for constraint 2 and 3 because both
pass through the origin some other point will be selected. The goal of the problem is to reduce the
valve of Z. The optimal solution is the intersection of the two lines x1+x2=800 and .21x1-.3x2=0
which yields x1= 470.59 and x2= 329.41 Ib. The minimum cost is $437.65 per day.
Conclusion:
We can solve probems easily on TORA and it is very helpful
Syed murad ali shah 17pwind0485 OR lab