**MAASAI MARA UNIVERSITY**

**REGULAR UNIVERSITY EXAMINATIONS**

**2015/2016 ACADEMIC YEAR**

**THIRD YEAR FIRST SEMESTER**

**SCHOOL OF BUSINESS & ECONOMICS**

**BACHELOR OF ECONOMICS**

**COURSE CODE: ECO 314**

**COURSE TITLE: QUANTITATIVE METHODS I**

**DATE: 6TH MAY 2016 TIME: 11-1 PM**

**INSTRUCTIONS TO CANDIDATES**

**Answer Question ONE and any other THREE questions**

**This paper consists of 4 printed pages. Please turn over.**

** **

**QUESTION ONE (25 MARKS)**

A manufacturer produces three products X, Y and Z. During production, the products require the use of two machines, A and B. The number of hours neeeded on both machines are shown in the following table

Machine A and B can be used for 40 hours and 34 hours a week respectively. the profits per unit is sh 10, sh 15 and sh 22 for product X , Y and Z respectively.

Formulate the linear Programing problem (3 Marks)

Solve the linear programming problem in a) above (12 Marks)

State and explain the assumptions for the input-output models (6 Marks)

Determine the functional dependence of the following functions

Y_1=〖3x〗_1^2+〖2x〗_2^2

Y_2=〖5x〗_1+1 (4 marks)

**QUESTION TWO (15 MARKS)**

Differentiate the following terms

Mutually exclusive Events and collectively Exhaustive events (2 marks)

Sample space and experiment (2 Marks)

Solve the following three simultaneous equations using the gaussian method.

2X+12Y-2Z=20

2X+3Y+3Z=17

3X-3Y-2Z=-9 (8 marks)

Differentiate the three approaches to probability (3 marks)

**QUESTION THREE (15 MARKS)**

Given the linear programing problem below, form its dual problem

250 members of a certain society have voted to elect a new chairman. Each member may vote for either one or two candidates. The candidate elected is the one who polls most votes. Three candidates x, y z stood for election and when the votes were counted, it was found that:

59 voted for y only, 37 voted for z only

12 voted for x and y, 14 voted for x and z

147 voted for either x or y or both x and y but not for z

102 voted for y or z or both but not for x

Required

Express the above information in a venn diagram (3 marks)

What is the probability that voters voted for x only? (2 marks)

What is the probability that voters voted for y? (2 marks)

What is the probability that voters voted for z? (2 marks)

What is the probability that a voter did not vote? (2 marks)

**QUESTION FOUR (15 MARKS)**

Out of 3000 tires in a warehouse, 2000 are domestic and 1000 are imported. Among the domestic tires, 40 % are all season and for the imported tires, 10% are all season. If a tire is selected at random and it is all-season, what is the probability that it is imported. (4 marks)

the IQs of a large population of children are normally distributed with a mean of 100.4 and a standard deviation of 11.6.

what percentage of children have IQs greater than 125?

(4 Marks)

90% of the children have IQs greater than what value?

(3 marks)

A commitee has 7 members, 3 men and 4 women. In how many ways can a sub commitee of four be selected if it is to consist of exactly

Three men (1 Mark)

Four women (1 Mark)

Two men and Two women (2 Mark)

**QUESTION FIVE(15 MARKS)**

The input-output ratio coefficients for a three sector economy are given as:

Determine the total output required in each of the three sectors to meet the inter-industry input requirements and the final demand. (9 marks)

In a survey of 150 people, each person was asked his/her marital status and their opinion about floating a bond issues to build a community centre. The results are summarised as follows

Find the probability that

A person favours the bond issue, given that the person is married (3 marks)

A person is married, given that the person favours the bond issue (3 marks)