More Subjects
[Name of the Writer]
[Name of Instructor]
MANAGEMENT SCIENCES
[Date]
Linear Programming Modeling Using Excel
For each case of large cups
Labors= 0.75 hours/ case
Materials= 16 Units/ case
For each case of small cups
Labors= 1 hoursper case
Materials= 11 Units per case
Labor
Material
Profit
X
0.75
16
35
Y
1
11
30
Total
120
2000
0.75x + Y =120equation 1
16x + 11y =2000equation 2
X ≥ 0
Y ≥ 0
To find the value of x multiply equation 1 by 11
8.25x + 11y = 1320equation 3
Now subtract equation 3 from equation 2
16x + 11y = 2000
-8.25x -11y = -1320
7.75x = 680
X = 87.74
To find the value of y put the value of x in equation 1
0.75 * 87.74 + y = 120
65.8 + y = 120
Y= 54.2
At Constraint 1 (C1) for equation 1
if the value of x is zero y will be 120
and if the value of y is zero x will be 160
C2 for equation 2
If value of X is zero y will be 181.81
And if Y is zero the value of x will be 125.
The graphical representation of these values is as under.
The highest profit is at the point of intersection of these two lines,at this point the value of X is 87.7 and the value of Y is 54.2, so the profit at this point will be:
Profit= 35x + 30y
Profit = (35 * 87.7) + (30 * 54.2)
Profit = $ 4685.5
So the profit at this point is $ 4685.5
Lets find the profit at other points
Profit (0,0) = 35 * 0 + 30 * 0
Profit (0,0) = 0
Profit (125,0) = 4375
Profit (0, 120) = 3600
So the maximum profit is at the point of intersection.
The optimal solution will be the same as the maximum profit. At this point, the company can earn maximum profit.
The binding constraints in this question are both the constraints because the slack value for both equations is zero.
To find the binding constraint put the values of x and y in both equations.
0.75x + y = 120
0.75 (87.7) + 54.2 + S1 = 120
65.8 + 54.2 + S1 = 120
120 + S1 = 120
So S1 = 0
In equation 2 put the values of x and y we get:
(16 * 87.7) + (11 * 54.2) + S2 = 2000
1403.6 + 596.4 + S2 = 2000
2000 + S2 = 2000
So the value of S2 is 0, hence it proved that both the constraints are bindings.
More Subjects
Join our mailing list
© All Rights Reserved 2023