TR ( total revenue ) = P ( price ) x Q ( quantity ) = ( 50 - 5 x² ) · x
TR = 50 x - 5 x³
Profit = TR - TC ( total cost ) = 50 x - 5 x³ - 30 x = - 5 x³ + 20 x
If x = 1 ( 1 million hoops ):
15 = - 5 · 1³ + 20 · 1 = - 5 + 20
If we want to find another production that makes the same profit:
15 = - 5 x³ + 20 x
5 x³ - 20 x + 15 = 0 / : 5
x³ - 4 x + 3 = 0
( x - 1 ) ( x² + x - 3 ) = 0
\(x_{12} = \frac{-1+ \sqrt{1+12} }{2}= \frac{-1+ \sqrt{13} }{2}\)
x ≈ 1.3
Answer:
A ) 1.3 million hoops
