Decision Analysis and Modelling

1
DECISION ANALYSIS AND MODELLING
Student’s Name
Code + Name of Course
Professor’s Name
University
City (State)
Date

2
Question 1
Primal model
Primal form of linear programming is the original form of linear programming. In this case lets
lettuce be x and tomato be y. The linear model will be
Min z=100 x +20 y
Subject to
2 x+ y ≥ 8
2 x+2 y ≥10
x , y ≥ 0
Using graphical technique, we draw the graph of the model as presented in the diagram below.
From the graphical solution of linear program designed above the optimal point will be at x = 0
and y = 8. The salad should thus e composed of only 8 grams of tomato. This will cost 160Rs
which is the minimal cost possible under the given constraints.
Dual form
This is another linear program problem that is related to the primal model. It will be designed as
follows.
Max ; Z=8 x +10 y

3
Subject to
2 x+2 y +w ≤ 100
x +2 y + z ≤20
Solving the dual model gives the solution presented by the table below.
From this solution, it’s evident that the cost will be 160Rs. This is similar to the optimal solution
of the primal model hence the linear model is proved to be the dual of the initial model.
Question 2
Developing a multiple linear regression model