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### Replies to This Discussion

Let we assume:
Boeing 757 be ‘x’
Boeing 767 be ‘y’
Boeing 777 be ‘z’

x y z Total seats
Tourist 50 75 40 305
Economy class 30 45 25 185
First class 32 50 30 206

We have got three equations:

50x + 75y +40z = 305 ………….. (1)
30x + 45y+ 25z= 185 …………… (2)
32x+ 50y+ 30z = 206 …………… (3)

solving equation (1) & (2)

50x + 75y +40z = 305
30x + 45y+ 25z= 185
multiply equation (1) by 3, and equation (2) by -5, we will get:

150x+ 225y+ 120z = 915
-150x- 225y- 125z = -915
-5z = -10

z= 2

now put z=2 in equation (3), we will get
32x +50y = 146
x = 146-50y …….. (a) ( continued)
32
put equation (a) in equation (1)

50x + 75y +40z = 305 ………….. (1)

50(146-50y ) + 75y +40(2) = 305
32
As z=2, put ‘z’ in above equation.
Solving the above equation we will get
y=1

put y=1 & z= 2 in equation (2)

30x + 45y+ 25z= 185 …………… (2)

30x + 45(1) + 25(2)= 185
30x = 185-95
30x= 90
x= 3

The company should fly:
3 Boeing 757
1 Boeing 767
2 Boeing 777
To fill all the seats each kind of plane should the company fly:
Boeing757 3 Planes
Boeing767 1 Plane
Boeing777 2 Planes
PLANES Eco. Class First Class Tourist
Boeing757 30*3=90 32*3=96 50*3=150
Boeing767 45*1=45 50*1=50 75*1= 75
Boeing777 25*2=50 30*2=60 40*2= 80
Reservations 185 206 305

AX=B

50 75 40 x1 305
30 45 25 x2 = 185
32 50 30 x3 206

50 75 40
│A│ = 30 45 25
32 50 30
│A│= 50(45*30 -25*50) - 75(30*30-25*32) + 40(30*50-45*32
= 50(1350-1250) - 75(900-800) + 40(1500-1440)
= 50(100) - 75(100) +40(60)
= 5000 -7500 +2400
= 7400 -7500
= -100

305 75 40
│A1│= 185 45 25
206 50 30
│A1│= 305(45*30-25*50) -75(185*30-25*206) +40(185*50-45*206)
= 305(1350-1250) -75(5550-5150) +40(9250-9270)
= 305(100) -75(400) +40(-20)
= 30500 -30000 -800
= 30500 -30800
= -300

50 305 40
│A2│= 30 185 25
32 206 30
│A2│= 50(185*30-25*206) -305(30*30-25*32) +40(30*206-185*32)
= 50(5550-5150) -305(900-800) +40(6180-5920)
= 50(400) -305(100) +40(260)
= 20000 -30500 +10400
= 30400 -30500
= -100

50 75 305
│A3│ = 30 45 185
32 50 206

│A3│= 50(45*206-185*50) -75(30*206-185*32) +305(30*50-45*32)

= 50(9270-9250) -75(6180-5920) +305(1500-1440)
= 50(20) -75(260) +305(60)
= 1000 -19500 +18300
= 19300 -19500
= -200

x = │A1│/│A│
= -300 / -100

y= │A2│/│A│
= -100 / -100

z = │A3│/│A│
= -200 / -100
x= 3, y=1, z= 2
To fill all the seats each kind of plane should the company fly:
Boeing757 3 Planes
Boeing767 1 Plane
Boeing777 2 Planes

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