Question

1. Find the inverse of the 3 by 3 matrix :

[123]
[014]
[560] by elementary row operations

2. A couple would like to invest $150,000 so that they can earn $8500 in interest in one year. One investment portfolio option suggest investing their money

into two accounts. One account earns interest at 7.5% and the other earns interest at 5%. How much should be invested in each account?

3. Given the following maximum problem, set up the initial simplex tableau and circle the first pivot element. Do not solve the maximum problems

MAXIMIZE : P = 3x1+2x2+3x3

subject to constraints : -x1+2x2+2x3<=8

4x1-x2+6x3<=10

x1+2x2+4x3<=12, x1>=0, x2>=0, x3>=0

4.Consider the following tableau. Determine the first pivot element and perform all the pivot operations for the entire pivot column.

Then, classify the tableau that results as one that is either "solved" or one that has "no solution" or one that is "ready for another set of pivot operations"

p y1 y2 y3 s1 s2 RHS

0 2 2 0 -1 1 36

0 2 2 0 -1 1 14

ㅡㅡㅡㅡㅡㅡㅡㅡㅡㅡ

1 5 -2 0 6 -1 9

Answer 1