quantitative analysis for business, 4 questions to be solved

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Question 1: Based on what you have studied about Quantitative Analysis, answer the following questions : (10 marks)

a.Discuss 4 techniques to solve decision problems under uncertainty. (2 marks)

b.A shipping company manager wants to determine the best routes for the trucks to take, to reach their destinations. Explain what type of model and type of method would you use to solve the problem? And why? (3 marks)

c. Possible problems in the Quantitative Analysis Approach could happen while acquiring input data. Gathering the data to be used in the problem solving is often not a simple task. In this context, from the internet search engines, discuss in details the two problems (Using Accounting Data – Validity of Data) that face managers while they obtain accurate input data and give your opinion on how you may solve those two problems. (5 marks)

Question (2): Solve the following problem: (10 marks)

The Feed Ranch fattens cattle for farmers and ship them to markets. The owners of the ranch seek to minimize total feed costs. The cost per pound of stocks X, Y are $5 and $7 respectively. The feed mix can be made up of the three grains that contain the following ingredients per pound of feed:

a)Formulate the problem as linear program. No graph is required. (4 marks)

b)Determine the optimal point that will minimize cost using the corner point method.

(3 marks)

c)Suppose that there had been a constraint that required the total number of Stock X and Stock Y combined to be 10 Feed. What would be the surplus? (Support your answer by explaining the term surplus). (3 marks)

Question (3): Referred to what you have learned about quantitative analysis models, answer the following problem (10 marks)

Suppose that Starbucks café wants to assign new hired workers (Ali, Hussein, and Fahad) to three different branches in (Juffair, City Centre mall, Diplomatic area). The entries in the table denote the costs of assigning the hired workers to a particular branch.

Required:

a-Formulate the above problem as a linear program. ( 2 marks)

b-Draw the network diagram for the problem. (1 marks)

c-Use the Hungarian method to find the optimal solution. (2marks x 3 tables= 6 marks)

d-Calculate the total cost of assigning. (1 mark)

Question (4): Answer the following problem (10 marks)

Dairy Drink Investment incorporated is investing money in stocks of companies producing drinks. It plans to invest 2 shares and 1 Government bond and wants to maximize the annual return of the portfolio.

Constraints:

1-The company plans to invest $250 000.

2-No more than $25 000 might be invested in milk shares.

3-Government bonds should cover at least 20% of all investments.

Formulate using Linear Programming to demonstrate the following:

a- Decision variables. (2 mark)

b- Objective function. (2 mark)

c- Constraints. (6 marks)