This question bugs me. I don't know how to get started. The teacher gave us a chart. We have to do 3 things.

• 1. define 3 variables
  2.write system of linear equations in 3 variables relating to known quantities and variables.
  3.solve for the variables

the chart was for dress shirts,dress slacks and suit jackets.
it also involved cutting,sewing and packaging.
for dress shirts
cutting took 15 minutes
sewing took 30 minutes
packaging took 12 minutes
for dress slacks
cutting took 10 minutes
sewing took 24 minutes
packaging took 6 minutes
for suit jackets
cutting took 20 minutes
sewing took 60 minutes
packaging took 5 minutes
man-hours available(hours) for all 3
cutting took 115 hours
sewing took 280 hours
packaging took 65 hours
Question to answer was how many of each of these items should you make to utilize all available man-hours of labor?

I know the variables are x,y, and z but what would the represent and how to I make the equations.

Everything you need is in the text of the problem. Let's consider cutting. Total cutting time is 115 hrs. This includes cutting shirts, slacks and jackets. We do not know how many of each was cut at this point, because this is what we have to find. So, let's assume the number of shirts cut is x, the number of slacks cut is y, and the number of jackets cut is z. It well may be that in the end some of the unknowns will turn out to be zero, but this is not important at this point. We just assign three variables. How many hrs does it take to cut x shirts? It is x*(1/4)hr. 15 min is 0.25 hr. How many hrs does it take to cut y slacks? y*(1/6)hr. HOw many hrs does it take to cut jackets? It is z*(1/3)hr. How long does the entire cutting job for all three items take? (1/4)x + (1/6)y + (1/3)z = 115. Here you go with your first equation. You have two more to construct, which is done similarly. Note that you use the same x, y, and z for the other two equations, because you assume that whatever was cut was also sewn and packaged. After you have three equations you solve this system of three equations to get x, y, and z. Remember that x, y, and z have to be >= 0. HTH

They are called simultaneous equations. Do a Google search for more info on how to.

Its just the forming of the equations that are sometimes difficult

-Cheers.

x-2y+z=8
2x+y-z=0
3x-6y+3z=24

Quote:

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Originally Posted by tatianna

x-2y+z=8
2x+y-z=0
3x-6y+3z=24

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