Consider the following which represents the equation for a production possibility frontier: y = - (¼) x 2 – (½) x + 42 where y is the quantity of industrial goods and x is the quantity of agricultural goods. What would be the quantity of agricultural goods if this country were to produce no industrial goods?
0 = - (¼) x^ 2 – (½) x + 42, solve for x
Solve for x:
0 = -x^2/4-x/2+42
0 = -x^2/4-x/2+42 is equivalent to -x^2/4-x/2+42 = 0:
-x^2/4-x/2+42 = 0
The left hand side factors into a product with four terms:
-1/4 (x-12) (x+14) = 0
Multiply both sides by -4:
(x-12) (x+14) = 0
Split into two equations:
x-12 = 0 or x+14 = 0
Add 12 to both sides:
x = 12 or x+14 = 0
Subtract 14 from both sides:
Answer: |x = 12 or x = -14
