Reference no: EM132876509
MA609 Business Analytics and Data Intelligence - Melbourne Institute of Technology
Learning Outcome 1: Demonstrate advanced and integrated understanding of business and data Intelligence for organisational decision-making.
Learning Outcome 2: Analyse critically, reflect on and synthesise techniques of data visualisation and data mining.
Assignment Description:
The assignment is designed to allow you to demonstrate effective business analytics skills using optimisation methods. You will need to use linear programming skills to conduct the analytics and obtain the solutions. This is individual assignment and each student will work independently.
Problem 1: Three objective functions for linear programming problems are 7A+10B=420 6A+4B=420, and -4A+7B=420. Show the graph of each for objective function values equal to 420.
Problem 2: Consider below the linear programming problem:
Max 3A+2B
s.t.
1A+1B≤10
3A+1B≤24
1A+2B≤16
A,B≥0
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Constraint
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Constraint R.H. side
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Allowable increase
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Allowable decrease
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1
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10
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1.20
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2
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2
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24
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6
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6
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3
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16
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Infinite
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3
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The value of the optimal solution is 27. Suppose that the right-hand side for consraint1 is increased from 10 to 11.
First find the optimal solution and draw the relevant graph. Then use the graphical solution procedure to find the new optimal solution by drawing the fourth line in the same graph.
Use the solution to part (a) to determine the shadow price for constraint 1.
The sensitivity analysis for the linear program in this problem provides the following right-hand side range information:
What does the right-hand side range information for constraint 1 tell you about the shadow price for constraint 1?
The shadow price for constraint 2 is 0.5. Using this shadow price and the right-hand-side range information in part (c), what conclusion can you draw about the effect of changes to the right-hand side of constraint 2?
Problem 3: Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below.
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Fliptop Model
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Tiptop Model
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Available
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Plastic
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3
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4
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36
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Ink Assembly
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5
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4
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40
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Molding Time
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5
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2
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30
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The profit for either model is $1000 per lot.
What is the linear programming model for this problem (write objective function and constraints?
Show the solution graphically.
Let F= the number of lots of Fliptop pens to produce
Let T= the number of lots of Tiptop pens to produce
Problem 4: For this problem:
Solve the following linear program graphically and,
Show the feasible region and,
Show the optimal point.
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Max
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5X + 7Y
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s.t.
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X ≤ 6
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2X + 3Y ≤ 19
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X + Y ≤ 8
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X, Y ≥ 0
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Attachment:- Business Analytics and Data Intelligence.rar