Question

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.

Answer 1

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