Assignment

Quantitative methods UGBS 301

Assignment 1

Instructions: This assignment is due on or before 14/09/2015 at 11:59 pm. All responses are

to be typed nicely in MS word and submitted through your drop box in Sakai.

Question 1

A farmer has 10 acres to plant wheat and cassava. However, he has $1200 to spend and each acre

of wheat costs $200 to plant and each acre of cassava costs $100 to plant. Moreover, the farmer

has to get the planting done in exactly 12 hours but it takes an hour to plant an acre of wheat and

2 hours to plant an acre of cassava. Assuming all the available acres and money has to be spent,

answer the following questions:

a. Write down all the linear equations in the problem above

b. Convert the equation into a Matrix Form

c. Using the Gauss-Jordan method, find the number of acres to be given to the planning of

wheat and cassava

Question 2

31 + 42 + 53 = −3

51 − 22 − 33 = 25

91 − 2 + 43 = −25

a. Express this in an augmented matrix form

b. Find values of 1 , 2 , and 3 in the systems of linear equations using the Elementary Row

Operations (ERO). Hint Gauss-Jordan Method.

Question 3

Find the inverse of the matrix below using the ERO approach. Show step by step how you arrive

at your answer.

4

-1

2

1

-4

1

2

0

2

1

1

-2

1

0

2

1

Questions 4

A manufacturing firm produces two products. Each product must undergo an assembly process

and a finishing process. It is then transferred to the warehouse, which has space for only a limited

number of items. The firm has 80 hours available for assembly and 112 hours for finishing, and it

can store a maximum of 10 units in the warehouse. Each unit of product 1 requires 4 hours to

assemble and 14 hours to finish. Each unit of product 2 requires 10 hours to assemble and 8 hours

to finish. The firm wants to determine the quantity of each product to produce.

a. Formulate the systems of linear equation for this problem.

b. Determine how many of each type product to produce using the inverse of the matrix in

(a) above....