### Understanding and application of Mathematical concepts

MASC20004 Quantitative Methods for Business - Middle East College

Learning Outcome 1: Make decisions under different environments.

Learning Outcome 2: Schedule and manage projects by using PERT and CPM.

Learning Outcome 3: Tackle simulation games by using various strategies.

Assignment Objective

1. To test the understanding and application of Mathematical concepts learning.

2. To test the calculation skills and Mathematical modelling ability of the learner.

3. To test the knowledge acquired by the learners on using statistical test and ability to infer on the outcomes.

Use the suitable resources to find the solution of the following problems.

Submit the answers neatly typed as per the specifications given below:

Problem 1. Assume that you are planning to go for a Medical tour to Thailand. Describe ( 200 -250 words) how you plan your trip. List atleast 6 activities involved in it. Estimate the time required to complete each activity by properly doing a research in internet. Cite the internet resources and give the references. Write the predecessor relations among the activities in a tabular form.

Problem 2. Sulaiman is planning to take his car for regular service. The work required in servicing is divided into several activities and represented in the below table along with the time taken for each task:

 ACTIVITY TASK Activity   symbol IMMEDIATE   PREDECESSORS Duration (min) Open the petrol tank cap A - a+1 Add petrol (Paid service) B A b+5 Close the petrol tank cap C B d+1 Open bonnet, check and add engine oil (Paid service) D - d+10 Check radiator coolant, Check battery, Close bonnet E D e+8 Clean the wind shield, Check air pressure in tires F - f+6 Prepare bill G B, E a+e+6 Collect payment H G a+b+5

Draw the network diagram and find the earliest start and latest finish time of all the activities. Also determine the total project time for which Sulaiman will stay at the service station and list out the critical activities.

Problem 3. Ali have been invited to play the Wheel of Fortune game on television. The wheel operates electronically with two buttons that produce hard (H) and soft (S) spin of the wheel. The wheel itself is divided into white (W) and red (R) half-circle regions. The wheel is designed to stop with a probability of (c+d+f)/30 in the white region. There is no chance 30 that the wheel will stop inbetween two regions. The payoffs of the game are:

 Alternatives States of nature W (R.O.) R (R.O.) H 800 200 S -2500 1000 Probabilities 0.3 0.7

Draw the associated decision tree and specify the course of action.

Problem 4. The research department of company has recommended to the marketing department to launch three varieties of biscuits. The marketing manager has to decide one of the types of Biscuit to be launched under the following estimated payoffs for various levels of sales:

 Estimated levels of sales Type of Biscuit 15,000 10,000 5,000 Milk Biscuit 30 10 10 Digestive Biscuit 40 15 5 Cream Biscuit 55 20 3

What will be the marketing manager's decision under the following decision criteria's?

a. Pessimistic criterion
b. Laplace criterion

Problem 5. The owner of a boat has estimated the following distribution of demand for a particular kind of boat.

 No. demanded 0 1 2 3 Probability 0.1 0.2 0.3 0.4

Each boat costs him (c + d) rials and he sells them for (2 ∗ c + 2 ∗ d) rials each. Prices are given in hundreds rial units. Boats that are left unsold at the end of the season must be disposed off for (c + d - 2) rials each. How many should be stocked so as to maximize his expected profit?

Problem 6. Solve the following game for optimal strategy based on algebraic method.

 B1 B2 B3 A1 9 + a 12 + b 6 + c A2 1 - d -3 -2 A3 6 14 + ?? 7 + f

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