Question

A company manufactures three types of wooden chairs: the Kitui, the Goa, and the Santa Fe. To make a Kitui chair requires 1 hour of cutting time, 1.5 hours assembly time, and 1 hour of finishing time. A Goa chair requires 1.5 hours of cutting time, 2.5 hours of assembly time and 2 hours of finishing time. A Santa Fe chair requires 1.5 hours of cutting time, 3 hours of assembly time, and 3 hours of finishing time. If 41 hours of cutting time, 70 hours of assembly time, and 58 hours of finishing time were used one week, how many of each type of chair were produced.

Answer 1

Are you still trying to figure out this question?

Answer 2

Yes.

Answer 3

okay, the first thing you do is define variables that represent the number of a certain chair made

so x = number of Kitui chairs
y = number of Goa chairs
z = number of Santa Fe

Answer 4

You have three variables, which means you need three equations to solve the problem. You can get these equations by looking at the different hours needed to make each chair

For cutting time 1x +1.5y +1.5z = 41
because each Kitui takes 1 hr, each Goa 1.5 hrs, and each Santa Fe 1.5hr

Following so far? Could you get the other two equations?

Answer 5

Assembly equation: x+1.5y+1.5z=70
Finish equation: x+2y+3z=58

Answer 6

I made a mistake:
Assembly equation:1.5x+2.5y+3z=70

Answer 7

cool you got it, alright well from here you can solve the system of equations by substitution of elimination.

I'll try elimination and with these equations

x + 1.5y + 1.5z = 41
1.5x + 2.5y + 3z = 70
x + 2y +3z = 58

Ill subtract equation 1 from equation 3 to get rid of the x term

so x + 2y + 3z = 58
-(x+1.5y+1.5z) = -(48)

.5y +1.5z = 10

one second i need to figure out the rest haha

Answer 8

Okay

Answer 9

damn i dont know where i messed up but ill write a quick summary to the right answer

Answer 10

I'm trying to figure this out through matrix...

Answer 11

I've plugged in the equation to some online matrix solvers and they all have said it has no solution.. something is off, blah I think you should work on another problem if you havent already. I want to figure this out

Answer 12

these people even seem to have the same problem http://openstudy.com/study#/updates/4fc4321be4b0964abc86cb98

Answer 13

I've tried to solve this changing the hours to minutes and putting them into my graphing calculator, but it says that it's not possible too.

Answer 14

hes just went offline, i say skip the problem since somethings wrong with it

Answer 15

Thanks anyway :)

Answer 16

confirmed:no solutions to those equations.
equations formed are correct though.

Answer 17

Thanks :) I'll let my teacher know.

Answer 18

ok. and welcome :)