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, 6A+4B, and -4A+7B. Show the graph of each for objective function values equal to 420.
Problem 2: Identify the feasible region for the following set of constraints:
3A - 2B ≥ 0
2A - 1B ≤ 200
1A ≤ 150
A, B ≥ 0
Problem 3: Consider below the linear programming problem:
Max 3A+2B
s.t.
1A + 1B ≤ 10
3A + 1B ≤ 24
1A + 2B ≤ 16
A, B ≥ 0
The value of the optimal solution is 27. Suppose that the right-hand side for consraint1 is increased from 10 to 11.
a. Use the graphical solution procedure to find the new optimal solution.
b. Use the solution to part a to determine the shadow price for constraint 1.
c. The sensitivity analysis for the linear program in this problem provides the following right-hand side range information:
|
Constraint
|
Constraint R.H. side
|
Allowable increase
|
Allowable decrease
|
|
1
|
10
|
1.2
|
2
|
|
2
|
24
|
6
|
6
|
|
3
|
16
|
Infinite
|
3
|
What does the right-hand side range information for constraint 1 tell you about the shadow price for constraint 1?
d. 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?
Note - Need to submit the assignment as a word document.
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