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Question 437217: A farmer has 200 hectares of land suitable for cultivating crops A, B, and C. The
cost of cultivating each crop is
• $40 per hectare for crop A
• $60 per hectare for crop B
• $80 per hectare for crop C
The labour hours required for each crop are
• 20 labour hours per hectare for crop A
• 25 labour hours per hectare for crop B
• 40 labour hours per hectare for crop C.
The farmer has 200 hectares of land, a budget of $12600, and a workforce that can
work a total of 5950 labour hours. How many hectares of each crop should he plant
to use up all his available land, budget, and labour hours?
[Hint: land, budget and labour correspond to 3 linear equations]
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Crop A - x
Crop B -y
Crop C-z
x+y+z=200.....................1
40x+60y+80z= 12600.............2
20x+25y+40z=5950...............3
consider equation 1 &2 Eliminate y
Multiply 1 by -60
Multiply 2 by 1
we get
-60x-60y-60z=-12000
40x+60y+80z=12600
Add the two
-20x+20z=600 -------------4
consider equation 2 & 3 Eliminate z
Multiply 2 by -5
multiply 3 by 12
we get
-200x-300y-400 z=-63000
240x+300y+480z= 71400
Add the two
40x+80z=8400 -------------5 5
Consider (4) & (5) Eliminate z
Multiply 4 by 2
Multiply (5) by 1
we get
-40x+40z=1200
40x+80z=8400
Add the two
120z=9600
/120
z=80
Plug the value of z in 5
40x+6400=8400
40x=2000
x=50
plug value of x & z in 1
50+y+80=200
y=-50-80+200
y=70
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