SOLUTION: A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hrs to prep, 2 hrs to paint, and 10 hrs to fire. A tree takes 16 hrs to prep 3 hrs to

Question 1179765: A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hrs to prep, 2 hrs to paint, and 10 hrs to fire. A tree takes 16 hrs to prep 3 hrs to paint, and 4 hrs to fire. A sleigh takes 4 hrs to prep, 14 hrs to paint, and 7 hrs to fire. If the workshop has 117 hrs for prep, 85 hrs for painting, and 118 hrs for firing, how many of each can be made? I can get the 3 equations and draw the matrix but now I am lost!
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hrs to prep, 2 hrs to paint, and 10 hrs to fire. A tree takes 16 hrs to prep 3 hrs to paint, and 4 hrs to fire. A sleigh takes 4 hrs to prep, 14 hrs to paint, and 7 hrs to fire. If the workshop has 117 hrs for prep, 85 hrs for painting, and 118 hrs for firing, how many of each can be made? I can get the 3 equations and draw the matrix but now I am lost!
wreaths, trees, and sleighs
prep 3 16 4 = 117

paint 2 3 14 = 85
fire 10 4 7= 118
3w+16t+4s=117
2w+3t+14s=85
10w+4t+7s=118
w=7,t=5,s=4
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

If you can construct a matrix equation model for this problem, it is great (!).

To move forward and solve the system, there are 3 major ways.

First way is to do it manually.
For it, you should know HOW TO do it.
There are different methods of manual solving: Substitution, Elimination and the Determinant method (same as the Cramer's rule).

You may learn about these methods from the lessons

    - Solving systems of linear equations in 3 unknowns by the Substitution method,
    - BRIEFLY on solving systems of linear equations in 3 unknowns by the Substitution method,
    - Solving systems of linear equations in 3 unknowns by the Elimination method
    - BRIEFLY on solving systems of linear equations in 3 unknowns by the Elimination method

    - Determinant of a 3x3 matrix
    - Co-factoring the determinant of a 3x3 matrix
    - HOW TO solve system of linear equations in three unknowns using determinant (Cramer's rule)
    - Solving systems of linear equations in three unknowns using determinant (Cramer's rule)
    - Solving word problems by reducing to systems of linear equations in three unknowns

in this site.

Another way is to solve your system using your pocket calculator.
You may learn on HOW TO do it from the numerous lessons and video presentations in the Internet.

            Put these keywords to the GOOGLE search engine "how to solve matrix equation using calculator",
            and it will provide you numerous useful links.

The third way is to solve your system using free of charge (!) online solver in the Internet.

            For it, put these keywords to the GOOGLE search engine "how to solve matrix equation using online solver",
            and it will provide you several useful links for this technology.

So many ways are there around you to improve and develop your skills (!)

If you chose some of these ways, you may report me about your progress.

It would be interesting to me to learn about your experience and your progress (!)

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