Real World Analytics

Running head: Real World Analytics
Real world Analytics
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Real World Analytics2
Table of Contents
Answer to question 1.................................................................................................................................3
Answer to question 2.................................................................................................................................4
Answer to question 3.................................................................................................................................7
Answer to question 4...............................................................................................................................10
References................................................................................................................................................13

Real World Analytics3
Answer to question 1
1.a)
Linear programming is considered to be a programming model which is an algebraic description
which is the main aim that is to be maximize or minimize the constraint that need to be satisfied by the
variable. Linear programming techniques helps in improving the quality of decisions.
Linear programing has given a way to unify results which are the mechanism design from
disparate areas. Linear programming is another crucial and important part of mathematics that deals with
the study of optimization problem with the required number of constraints and objective. To find a point
which is in the polyhedron where the function has the smallest or it can be said that the largest value if
exist.
1.b)
Let x be the invested amount from factory A.
Let y be the invested amount from factory B.
To optimize Z=5x+8y
The recipes for the production of the new cheese require
30x+80y<=60
60x+40y>=45
40x+70y>=50
These are the restriction
Hence,
To optimize Z = 5x+8y
Subject to the constraints
30x+80y<=60
60x+40y>=45
40x+70y>=50
1.c)
To solve this problem let us consider the in equations as equations as follow:
30x+80y = 60 ...(1)
60x+40y = 45 ...(2)
40x+70y = 50 ....(3)
Now, putting these equations in graph, we have,

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Figure 1
The graph have been solved from online graph maker available
From the above graph, we can say the feasible region is ABCDA.
Now, we have the coordinates of A, B, C and D are (23/52 , 6/13), (1/3 , 5/8), (0 , ¾), (0 , 5/7)
respectively.
Now, at A, Z = 5*(23/52)+8*(6/13) = 5.90
At B, Z = 5*(1/3)+8*(5/8) = 6.67
At C, Z = 5*(0)+8*(3/4) =6
And at D, Z = 5*0 + 8*(5/7) = 5.71
Hence, D will be the minimum point.
It means, the optimum solution is (0 , 5/7)
Answer to question 2
2.a)
xc1/(xc1+xw1+xs1) Cotton in Spring =>y1>=0.5