Let the PPFs of the factories look like this:
1 plant: y = 40-x
2 plant: y = 100 - 4x
3 plant: y = 60 -2x
Find the maximum number of x if you want it to be exactly the same as y.
The set of equations are as follows
"y=50-x... equation 1"
"y=100-4x... equation 2"
"y=60-2x... equation 3"
Add the first two equations 1 and 2;
"(y=40-x )+(y=100-4x) =(2y=140-5x)"
Add equation 2 and 3;
"(y= 100-4x)+(y=60-2x) =(2y=160-6x)"
Such that you obtain two set of equations which are;
"2y=140-5x ... equation 4"
"2y=160-6x... equation 5"
Making y the subject from equation 4 you get;
"y =70-2.5x....equation 6"
Substituting for y in equation 5;
"2(70-2.5x)=160-6x"
Where you get "X=20"
Substituting for the value of x in equation 6;
"y=70-(2.5*20) =20"
"Answer = 20"
Units of x needed to produce the same number of y are 20
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