SBP manufactures three specialty detergent powders called Cleany, Shiny and Whity. The detergent powders have to go through three processes; Blending, Refining and Packaging. The following is the estimated profit and production hours for each process per kilogram of output for each of the three detergent powders: Process Cleany (hours) Shiny (hours) Whity (hours) Total hours Blending Refining Packaging 1 1.5 9,000 0.67 0.67 1 4,500 0.5 0.33 0.5 2,300 Profit RM10 RM15 RM14 The new management accountant of SBP has used a linear programming software to find the optimal solution to maximize profit. Table 1 presents the final matrix of the optimum solution from the software. Table 1 Final Matrix Basic variables S1 S2 S3 X2 = 2,250 -1 1.5 %3D X3 = 2,800 0.67 -4 4 %3D X1 = 300 3 -6 C = 75,950 -5.67 -3.5 -4 Note: X1 = Cleany; X2= Shiny; X3= Whity; S1 = Blending; S2 = Refining; S3 = Packaging; C = Profit Required: (a) Formulate the above data into a linear programming model that will maximize the profit for SBP. (b) Interpret the final matrix produced by the management accountant in Table 1. Include vour interpretation for column S1. (c) The management of SBP has decided to recruit new workers because of business expansion and to satisfy the market demand. This new recruitment contribute for 100 hours of packaging time. Determine the effect of the new recruitment on the final solution.
SBP manufactures three specialty detergent powders called Cleany, Shiny and Whity. The detergent powders have to go through three processes; Blending, Refining and Packaging. The following is the estimated profit and production hours for each process per kilogram of output for each of the three detergent powders: Process Cleany (hours) Shiny (hours) Whity (hours) Total hours Blending Refining Packaging 1 1.5 9,000 0.67 0.67 1 4,500 0.5 0.33 0.5 2,300 Profit RM10 RM15 RM14 The new management accountant of SBP has used a linear programming software to find the optimal solution to maximize profit. Table 1 presents the final matrix of the optimum solution from the software. Table 1 Final Matrix Basic variables S1 S2 S3 X2 = 2,250 -1 1.5 %3D X3 = 2,800 0.67 -4 4 %3D X1 = 300 3 -6 C = 75,950 -5.67 -3.5 -4 Note: X1 = Cleany; X2= Shiny; X3= Whity; S1 = Blending; S2 = Refining; S3 = Packaging; C = Profit Required: (a) Formulate the above data into a linear programming model that will maximize the profit for SBP. (b) Interpret the final matrix produced by the management accountant in Table 1. Include vour interpretation for column S1. (c) The management of SBP has decided to recruit new workers because of business expansion and to satisfy the market demand. This new recruitment contribute for 100 hours of packaging time. Determine the effect of the new recruitment on the final solution.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Transcribed Image Text:SBP manufactures three specialty detergent powders called Cleany, Shiny and Whity. The
detergent powders have to go through three processes; Blending, Refining and Packaging. The
following is the estimated profit and production hours for each process per kilogram of output for
each of the three detergent powders:
Process
Cleany (hours)
Shiny (hours)
Whity (hours)
Total hours
Blending
Refining
Packaging
1
2
1.5
9,000
4,500
2,300
0.67
0.67
1
0.5
0.33
0.5
Profit
RM10
RM15
RM14
The new management accountant of SBP has used a linear programming software to find the
optimal solution to maximize profit. Table 1 presents the final matrix of the optimum solution from
the software.
Table 1 Final Matrix
Basic variables
S1
S2
S3
| X2 = 2,250
X3 = 2,800
X1 = 300
C = 75,950
-1
1.5
0.67
-4
4
3
-6
-5.67
-3.5
-4
Note:
X1 = Cleany; X2= Shiny; X3= Whity; S1 = Blending; S2 = Refining; S3 = Packaging; C = Profit
Required:
(a)
Formulate the above data into a linear programming model that will maximize the profit
for SBP.
(b)
Interpret the final matrix produced by the management accountant in Table 1. Include vour.
interpretation for column S1.
(c)
The management of SBP has decided to recruit new workers because of business
expansion and to satisfy the market demand. This new recruitment contribute for 100
hours of packaging time. Determine the effect of the new recruitment on the final solution.
(d)
Briefly explain TWO (2) uses of linear programming model.
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