Question

Please help! Hi, I'm stuck on a part of this question, we have to solve using Gauss Jordan Elimination: A corporation wants to lease a fleet of 12 airplanes with a combined carrying capacity of 220 passengers. The three available types of planes carry 10,15,20 passengers. How many of each type of plane should be leased?

Answer 1

see assume like x,y,z
10x+15y+20z=220
x+y+z=12
and one more?

Answer 2

is that all?

Answer 3

I understood these parts until I solved using Gauss Jordan Elimination and got:
[1 0 1 | -8 ]
[0 1 2 | 20 ]
Here is the part where I didn't understand,
x + z = -8
y + z = 20
z = r
8≤ z ≤10?

Answer 4

oh ok.........wat did u not understand?

Answer 5

The 8 ≤ z ≤ 10, I'm not sure if this should be given or we have to find it out.

Answer 6

wat i thot was like we kno that x,y,z>=0 so....i thot we cn make smthin out of it
and is that answer correct?
i dont see how x+z=-8?
it's like the company is giving away planes?

Answer 7

Is there more than one solution for this?

Answer 8

it's obvious doncha think

Answer 9

They're leasing planes, and we need 12 planes, they should be a combination of 3 planes that carry either 10, 15 or 20 passengers. According to the answer there are multiple solutionsy, because it should be a combination. The final answer is; Either, z=8, x=0, y=4
or z=9, x=1, y=2, or z=10 x=2, y=0. The total of these 3 combinations is equal 12 and I understand that because z= r (Free variable) What's frustrating me it the 8≤ z ≤ 10.

Answer 10

z = 9, x = 1, y = 2 should be the only true solution.

Answer 11

i dont see why x/x cant be zero?

Answer 12

I think i got it! Could it be that because x= -8 + z and y= 20 - 2z
We solve by finding z which equals to z=8 and z=10, which means that the answer for z is 8≤ z ≤10! And then we substitute in the given equations to find how many planes we should lease! I think I got it :D

Answer 13

I just realized I said I think I got it twice. Lol, sorry. it's cause i've been stuck on it for a while.

Answer 14

Thank you so much for your help!