Kendall Square Inc makes and sells ramen to the large number of students around MIT. Kendall Square Inc uses the production function(,)=(+2)1/3 ( its raised to the power of 1/3)

. Input prices are=2

and=3

for labor and capital respectively. It operates in a perfectly competitive environment facing a price=$48

, and uses an initial amount of capital=12

What is the optimal output level for Kendall Square, Inc in the short run?

? = ?

What are its profits?

?= ?

Compute Kendall Square Inc's long-run cost function. To verify that you have the correct long-run cost function, calculate the long-run cost of producing 8 units of ramen.

?(8)= ?