# Systems of Linear equation/matrices problem. Need some help.

1. Sep 5, 2011

### nando94

I have this math packet for hw and it has loads of problems on systems of equations and matrix. The last few problems have been bothering me. Here it is:

To manufacture an automobile require painting, drying, and polishing. Epsilon Motor Company produces three types of cars: the Delta, the Beta, and the Sigman. Each Delta requires 10 hours of painting, 3 hours of drying, and 2 hours of polishing. A beta requires 16 hours of painting,, 5 hours of drying, and 3 hours of polishing, while the Sigma requires 8 hours of painting, 2 hours of drying, and 1 hours of polishing. If the company has 240 hours for painting, 69 hours for drying, and 41 hours for polishing per month, how many of each type of car are produced?

You have to solve it using system of linear equations and then using matrices. Since the matrix part might take time just give me some advice on how to set it up and ill do the math. Thanks.

2. Sep 5, 2011

### HallsofIvy

Let B be the number of "Beta" cars, S the number of "Sigma" cars, and D the number of "Delta" cars produced in a month.

Each "Beta" requires 16 hours of painting, each "Sigma" requires 8 hours of painting, and each "Delta" requires 10 hours of painting. That is, the total number of hours required to produce those cars is 16B+ 8S+ 10D and that cannot be more than 240 hours: $16B+ 8S+ 10D\le 240$.
In order to get a specific answer you will have to take $16B+ 8S+ 10D= 240$.

Do the same to get the equation for drying and polishing. That will give you three equations in three unknowns so you can set up the three by three coefficient matrix.