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# Matrices and their Applications

(See the Attached Questions File)

Answer all questions and show work

1. Find:

2. Find the inverse of:

3. Compute the transpose of A =

4. Introduce slack variables and set up the initial tableau. Do not solve.

Maximize
subject to the constraints

5. Find the Pivot element for

Do not Solve.

6. Find the solution of the following final tableau

7. Write the dual problem for the following. DO NOT SOLVE.
Minimize

subject to the constraints

8. A company makes three products, A, B, and C. There are 500 pounds of raw material available. Each unit of product A requires 2 pounds of raw material, each unit of product B requires 2 pounds of raw material, and each unit of product C requires 3 pounds of raw material. The assembly line has 1,000 hours of operation available. Each unit of product A requires 4 hours of assembly, while each unit of products B and C requires 5 hours. The company realizes a profit of \$500 for each unit of product A, \$600 for each unit of product B, and \$1,000 for each unit of product C. How many units of each of the products should the company make to maximize the profit? DO NOT SOLVE THIS PROBLEM. JUST SET UP THE PROBLEM AND WRITE THE INITIAL TABLEAU WITH THE SLACK VARIABLES.

Use the following to answer questions 20-22:

A \$152,400 loan is taken out at 11.5% for 25 years, for the purchase of a house. The loan requires monthly payments.

9. Find the amount of each payment.

10. Determine the total amount repaid over the life of the loan.

11. Find the total interest paid over the life of the loan.

#### Solution Preview

The solution file is attached.

Answer all questions and show work

1. Find:

Product = [■(1 * 4+3 * 0&1*3+3*1@2*4+ -1*0&2*3+ -1*1)]= [■(4&6@8&5)]

2. Find the inverse of:

The determinant of the given matrix is 2(-2) - (-1)3 = -4 + 3 = -1
Adjoint of the given matrix is [■(-2&-3@1&2)]
Inverse of the given matrix = Adjoint / Determinant = [■(-2&-3@1&2)] / -1 = [■(2&3@-1&-2)]

3. Compute the transpose of A =

Transpose is [■(2&1@3&-1@0&5)]

4. Introduce slack variables and set up the initial tableau. Do not solve.

Maximize
subject to the constraints

Initial Tableau:

5. Find the Pivot element for

Do not ...

#### Solution Summary

Neat and Step-by-step Solutions to all questions. Graphs (if any) are also included.

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