Application of LP in Manufacturing and Project Management

Running head: Application of LP in Manufacturing and Project Management
Project 1
Name of the Student
Name of the University
Author Note

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APPLICATION OF LP IN MANUFACTURING AND PROJECT MANAGEMENT
Question 9:
Given problem is
Maximize, Profit P = 10a + 15b + 22c + 17d
Where, a, b, c and d are the quantities of product 1, 2, 3 and 4.
The quantities must be less than the maximum demand of each product in the coming week.
Hence, a <= 50, b <= 60, c <= 85 and d <= 70.
The man-hours needed in three stages of 4 products are given by the following table.
20% of the man-hours which is previously employed in stage B can be employed in stage A
and 20% of the man-hours which is previously employed in stage C can be employed in stage
A.
The nominal time available till next week for every stage A, B, C is 160, 200 and 80 man-
hours respectively.
Hence,
2*a + 2*b + 3*c + 4*c + 0.2*(2a + 2b + 4c + 2d) + 0.3(a + 3b + 3c + d) <= 160
2a + 2b + 4c + 2d <= 200

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APPLICATION OF LP IN MANUFACTURING AND PROJECT MANAGEMENT
a + 3b + 3c + d <= 80
Product 1 units assembled / product 4 units assembled must be in between 0.9 and 1.15.
0.9 <= (a/d) <= 1.15
Or, a/d => 0.9 Or, a >= 0.9d Or, a – 0.9d >= 0
Or, a/d <= 1.15 Or, a <= 1.15d Or, a -1.15d <= 0
Hence, the linear programming problem is the following.
Objective function:
Max 10a + 15b + 22c + 17d
Subjected to Constraints:
a <= 50, b <= 60, c <= 85 and d <= 70
2*a + 2*b + 3*c + 4*d + 0.2*(2a + 2b + 4c + 2d) + 0.3(a + 3b + 3c + d) <= 160
2a + 2b + 4c + 2d <= 200
a + 3b + 3c + d <= 80
a – 0.9d >= 0
a -1.15d <= 0
Excel solver solution:

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APPLICATION OF LP IN MANUFACTURING AND PROJECT MANAGEMENT
Product 1 quantity Product 2 quantity Product 3 quantityProduct 4 qua
8 0 21 8
Profit(£) 678
Constraints
2*a + 2*b + 3*c + 4*c + 0.2*(2a + 2b + 4c + 2d) + 0.3(a + 3b + 3c + d) <= 160 157.9 <= 160
2a + 2b + 4c + 2d 116 <= 200
a + 3b + 3c + d 79 <= 80
a – 0.9d 0.8 >= 0
a -1.15d -1.2 <= 0
a >= 50 8 <= 50
b >= 60 0 <= 60
c >= 85 21 <= 85
d >= 70 8 <= 70
Sensitivity report:
Cell Name Origi
nal
Value
Final
Value
$B$7 Profit(£) Product 2 quantity 0 678
Cell Name Origi
nal
Value
Final
Value
Integ
er
$A$3 Product 1 quantity 0 8 Integ
er
$B$3 Product 2 quantity 0 0 Integ
er