May 28th, 2014, 03:28 PM  #1 
Newbie Joined: May 2014 From: east freedom pennsylvania Posts: 5 Thanks: 0  need help 2
You own a business that makes gaming software. Your company has decided to create 3 addon software options. To create these addons, it takes a team that consists of a computer programmer, graphic artist, and mathematician. • Addon software A takes the programmer 9 hours, the graphic artist 6 hours, and the mathematician 1 hour to complete. • Addon software B takes the programmer 10 hours, the graphic artist 4 hours, and the mathematician 2 hours. • Addon software C takes the programmer 12 hours, the graphic artist 4 hours, and the mathematician 1 hour. If there are 398 programming hours available, 164 graphic artist hours available, and 58 mathematician hours available, how many copies of each software can be produced? Use the following guidelines for your answer: • Set up the systems of equations. • Solve the system of equations, using any preferred method for solving. 
May 28th, 2014, 06:43 PM  #2 
Newbie Joined: May 2014 From: China Posts: 3 Thanks: 0 
I want to know whether it has some order for example we must finish A so we can do B later

May 28th, 2014, 08:24 PM  #3 
Newbie Joined: May 2014 From: east freedom pennsylvania Posts: 5 Thanks: 0  No Order
Was just given instructions of how many copies of each software 
May 29th, 2014, 06:38 AM  #4 
Senior Member Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40 
You'd have to be more specific. What if I was to decide not to produce add on software B or C? That would surely allow me to make more copies of add on software A, wouldn't it? I'm not a fan of these badly written maths problems. If a teacher has given you this question, then you should ask that teacher to rewrite the question. That would be a more promising mathematical solution. Last edited by perfect_world; May 29th, 2014 at 06:50 AM. 
May 29th, 2014, 07:20 AM  #5 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,161 Thanks: 734 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
The key word you are missing is 'maximum' number of copies of software by making best use of the time for each staff. Otherwise, this question is very clear. Equations can be formed that are based on the premise that every possible minute is spent by each team member performing work. So, assuming that no one spends time pissing about doing nothing, what is number of copies of A, B and C made that allow this? I have an answer... I'll post it in a few hours! 
May 29th, 2014, 07:26 AM  #6  
Senior Member Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40  Quote:
Last edited by perfect_world; May 29th, 2014 at 07:31 AM.  
May 29th, 2014, 07:40 PM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond 
9A + 10B + 12C = 398 6A + 4B + 4C = 164 A + 2B + C = 58 Using elimination of variables it can readily be determined that A = 6, B = 20 and C = 12. 
May 29th, 2014, 09:05 PM  #8 
Newbie Joined: May 2014 From: east freedom pennsylvania Posts: 5 Thanks: 0  Thanks
Awesome cd!

May 30th, 2014, 02:04 AM  #9 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,161 Thanks: 734 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
$\displaystyle \left( \begin{array}{ccc} 9 & 10 & 12 \\ 6 & 4 & 4 \\ 1 & 2 & 1 \end{array} \right) $$\displaystyle \left( \begin{array}{ccc} A \\ B \\ C \end{array} \right) = \left( \begin{array}{ccc} 398 \\ 164 \\ 58 \end{array} \right) $ Leftmultiplying both sides by the inverse gives $\displaystyle \left( \begin{array}{ccc} A \\ B \\ C \end{array} \right) = \left( \begin{array}{ccc} 9 & 10 & 12 \\ 6 & 4 & 4 \\ 1 & 2 & 1 \end{array} \right)^{1} \left( \begin{array}{ccc} 398 \\ 164 \\ 58 \end{array} \right) $. Using whichever method you prefer, the inverse of the matrix can be calculated to be $\displaystyle \frac{1}{40}\left( \begin{array}{ccc} 4 & 14 & 8 \\ 2 & 3 & 36 \\ 8 & 8 & 24 \end{array} \right)$, so $\displaystyle \left( \begin{array}{ccc} A \\ B \\ C \end{array} \right) =\frac{1}{40}\left( \begin{array}{ccc} 4 & 14 & 8 \\ 2 & 3 & 36 \\ 8 & 8 & 24 \end{array} \right) \left( \begin{array}{ccc} 398 \\ 164 \\ 58 \end{array} \right) = \left( \begin{array}{ccc} 6 \\ 20 \\ 12 \end{array} \right) $. 
May 30th, 2014, 02:53 AM  #10 
Senior Member Joined: Apr 2014 From: UK Posts: 963 Thanks: 342 
If they are making 3 addons, then the time to make 1 of each is all that's required, then just copy it 