Problem 1:

We need to build up to 6 power plants (L1 to L6) to serve 7 communities (C1 to C7). The cost to build a power plant is 6.5 million (AED). The maximum capacity of each plant is 11 million watts. The demand of each community is given below:
Community 1 2 3 4 5 6 7
Demand in millions watt 3 4 6 4 5 2 4

The benefits (in $/watt but sometimes it is a loss) from serving the community is given below:
Location C1 C2 C3 C4 C5 C6 C7

L1 4 4.5 2.5 1.5 3.5 4.2 -0.5
L2 4 4.5 2.5 0.5 1 0.5 -3.5
L3 3.5 5 4 1.5 4.5 3.5 0
L4 1.3 3 5 1.8 5.5 3.3 1.3
L5 0.5 1 1.5 5.5 4 5 3
L6 -1 0 1.5 4.5 4 3.3 2

Find which power plants should be built:

Problem 2:

    Company, which manufactures makes hockey sticks and chess sets. Each hockey stick yields an 
    incremental profit of $5, and each chess set, $5. 

• A hockey stick requires 6 hours of processing at Machine Center A and two hours at Machine Center B.
• A chess set requires 6 hours at Machine Center A, 8 hours at Machine Center B, and 2 hours at MachineCenter C.
• Machine Center A has a maximum of 60 hours of available capacity per day, Machine Center B has 36 hours, and Machine Center C has 10 hours. If the company wishes to maximize profit, how many hockey sticks and chess sets should be produced per day?

Answer the following:

a) Formulate the linear programming model to determine the optimal solution

b) Use Excel solver to generate the sensitivity report and Interpret the sensitivity report.

c) Use Solvertable to investigate further the sensitivity due to change in profits (discuss)

Problem 3

One set (1000 data points each) is generated from unknown population (saved in excel)

a) Use Arena Arena Tools  Input Analyzer to see the best fit (present your finding in a tabular form) which distribution fits best (show your work).

b) Fill out the following table for each list and for each of the three distribution the Chi-square goodness of fit. Use the chi-square fit.
List
Class Class Interval Uniform Normal Exponential
Observed frequencies Expected Expected Expected
Class 1
Class 2
Class 3 ….
Class 20
Chi2
Df n-r-1
p_value
decision
, n: # of classes 20-0 =20. r: # of constraints (r=0)

Part B (Arena Simulation)

Description

You are to propose a system to simulate. Implement an Arena solution to your proposed system. The simulation may relate to an existing system or to some proposed modification of given system.
The system may relate to manufacturing, service, health, transportation, …

Requirements:

• Problem statement : detail the proposed idea
• Short Introduction and Background (half a page 200-300 words)
• Related literature (half a page or 200-300 words)
• Description of the Arena simulation model
• Simulation detail (Doe(s)) and the animation that comes with the model. (describe and discuss the statistics)
• Discuss of simulation results (how the simulation had helped in exploring the solution)
• Conclusion (half a page 200-300 words)
• References