# Matrix Word Problem!!

• Feb 11th 2009, 04:59 PM
toiletking
Matrix Word Problem!!
You work for a company that has two pants (one in Tennessee and one in Colorado) that makes radios, tvs, and stereo systems. Each day the Tennessee plant can make 30 radios, 40 tvs, and 60 stereos at a cost of $1700 dollars per day. Each day the Colorado plant can make 40 radios, 70 tvs, and 30 stereo systems at a cost of$2300 dollars per day. One day your boss comes to you and says that the company has received an order for 5000 radios, 8000 tvs, and 4500 stereo systems. Your task is to find the number of days each plant should operate in order to meet the order at a minimal cost to the company. Also, What is the objective function?

I am just trying to figure out how to put this into matrix form, I want to say the system of equations is: 30x+40y+60z=1700 and 40x+70y+30z and from there I am not sure what to do, I know that I cant multiply a 2x4 matrix by a 3x1. I just need to know the steps on how to solve this.
• Feb 11th 2009, 11:15 PM
Matrix word problem
Hello toiletking
Quote:

Originally Posted by toiletking
You work for a company that has two pants (one in Tennessee and one in Colorado) that makes radios, tvs, and stereo systems. Each day the Tennessee plant can make 30 radios, 40 tvs, and 60 stereos at a cost of $1700 dollars per day. Each day the Colorado plant can make 40 radios, 70 tvs, and 30 stereo systems at a cost of$2300 dollars per day. One day your boss comes to you and says that the company has received an order for 5000 radios, 8000 tvs, and 4500 stereo systems. Your task is to find the number of days each plant should operate in order to meet the order at a minimal cost to the company. Also, What is the objective function?

I am just trying to figure out how to put this into matrix form, I want to say the system of equations is: 30x+40y+60z=1700 and 40x+70y+30z and from there I am not sure what to do, I know that I cant multiply a 2x4 matrix by a 3x1. I just need to know the steps on how to solve this.

Suppose the Tennessee plant works for $x$ days, and the Colorado plant for $y$ days. Then the total number of each item produced is given by the matrix equation:

$\begin{pmatrix}30&40\\40&70\\60&30\end{pmatrix}\be gin{pmatrix}x\\y\end{pmatrix} = \begin{pmatrix}5000\\8000\\4500\end{pmatrix}$

And the cost \$C is given by:

$\begin{pmatrix}1700&2300\end{pmatrix}\begin{pmatri x}x\\y\end{pmatrix} = \begin{pmatrix}C\end{pmatrix}$

Which can be combined into a single matrix equation as:

$\begin{pmatrix}30&40\\40&70\\60&30\\1700&2300\end{ pmatrix}\begin{pmatrix}x\\y\end{pmatrix} = \begin{pmatrix}5000\\8000\\4500\\C\end{pmatrix}$

Is that any help?