Reference no: EM132971484

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 objective function values on the same graph.

Problem 2: Consider below the linear programming problem. The formulation and sensitivity analysis output is given:

Minimize cost or z = 100x1 + 32x2 + 32x3 + 32x4 + 32x5 + 32x6

x1 ≤ 12 (Max. full-timers)
x1 + x2 ≥ 10 (9am to 10am)
x1 + x2 + x3 ≥ 12 (10am to 11am)
0.5x1 + x2 + x3 + x4 ≥ 14 (11am to noon)
0.5x1 + x2 + x3 + x4 + x5 ≥ 16 (Noon to 1pm)
x1 + x3 + x4 + x5 + x6 ≥ 18 (1pm to 2pm)
x1 + x4 + x5 + x6 ≥ 17 (2pm to 3pm)
x1 + x5 + x6 ≥ 15 (3pm to 4pm)
x1 + x6 ≥ 10 (4pm to 5pm)
4x2 + 4x3 + 4x4 + 4x5 + 4x6 ≤ 56 (Corporate policy)
x1, x2, x3, x4, x5, and x6 ≥ 0 (Non-negativity)

Answer below questions:
a. Identify the range of optimality for c1 (Salary per full-timer).
b. If c1 was increased to $10,000, would the current solution remain optimal?
c. Identify the range of feasibility for the right-hand-side value for "Corporate Policy" constraint.
d. How much personnel cost decrease if the right-hand-side value for "Corporate Policy" constraint was increased from 56 to 116?

Problem 3: Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below.

	Fliptop Model	Tiptop Model	Available
Plastic	3	4	36
Ink Assembly	5	4	40
Molding Time	5	2	30

The profit for either model is $1000 per lot.

a. What is the linear programming model for this problem (write objective function and constraints?

b. 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:
1. Solve the following linear program graphically and,
2. Show the feasible region and,
3. Show the optimal point.

Max 5X + 7Y
s.t. X ≤ 6
2X + 3Y ≤ 19
X + Y ≤ 8
X, Y ≥ 0

Attachment:- Business Analytics and Data Intelligence.rar