I need help solving a word problem using matrices.

Question

A ceramics workshop makes wreaths, trees and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint and 10 hours to fire. A tree takes 17 hours to prepare, 3 hours to paint and 4 hours to fire. A sleigh takes 4 hours to prepare, 14 hours to paint and 7 hours to fire. If the workshop has 124 hours for prep time, 75 hours for painting and 131 hours for firing, how many of each can be made?

Answer 1

First you can setup this sytem of equations

 

3*W + 17*T + 4*S = 124 (for total prep time)

2*W + 3*T + 14*S = 75 (total paint time)

10*W + 4*T + 7*S = 131 ( and for total firing time)

 

Then transfer that to matrix form

 

|  3  17  4 |    | W |    | 124 |

|  2   3 14 | * | T  | = |  75 |

| 10  4   7 |    | S |     | 131 |

 

or, A*x = B

 

Then you can just solve for x

 

x = B * (A)^(-1)

or use Cramer's rule or whatever you guys are studying at the moment.

 

I got

 

W = 9

T = 5

S = 3