Real World Analytics 1

Real World Analytics 1
REAL WORLD ANALYTICS
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Real World Analytics 2
Question 1
a)
Linear programming is the most suitable model to solve this case study because the case
study had an objective function which required minimization. Additionally, the case
study has several constraints to be satisfied for cost minimization.
b)
Let
X be the number of liter of product A
Y be the number of liter of product B
A B
Lime/ 100L 3 8
Orange/100L 6 4
Mango/100L 4 6
Cost/L 8 7
No. of liters x y
Objective function: 8x+7y
Constraints
6 x+ 4 y
100 ≥ 4.5
4 x +6 y
100 ≥ 5
3 x +8 y
100 ≤ 6
Customer needs: x+y≥ 70
The number of products A and B produced cannot be negative thus
x≥ 0
y≥ 0

Real World Analytics 3
Therefore, minimize 8x+7y
Subject to:
6 x+ 4 y
100 ≥ 4.5
4 x +6 y
100 ≥ 5
3 x +8 y
100 ≤ 6
x+y≥ 70
x≥ 0
y≥ 0
Changing the subject to y :
Y ≥ 450−6 x
4
Y ≥ 500−4 x
6
Y ≤ 600−3 x
8
y≥ 70-x
x≥ 0
y≥ 0
In desmos, we plot the opposite of the inequalities
Y ≤ 450−6 x
4
Y ≤ 500−4 x
6
Y ≥ 600−3 x
8

Real World Analytics 4
y≤70-x
x≤ 0
y≤ 0
c)
There are four points at the corner points of the wanted region which are likely to yield the
minimum cost. The points are:
(33.333,62.5)
(35,60)
(125,0)
(200,0)
To find the minimum points, objective function is evaluated at these four corner points
At (33.333,62.5),
Cost= 8x+7y= 8(33.333)+7(62.5) = 704.164