Kendall Square Inc makes and sells ramen to the large number of students around MIT. Kendall Square Inc uses the production functionF(K,L)=(K+2L)^(1/3). Input prices arew=2 andr=3for labor and capital respectively. It operates in a perfectly competitive environment facing a pricep=$48, and uses an initial amount of capitalK^=12.

What is the optimal output level for Kendall Square, Inc in the short run?, What are its profits in the short run?, and what is the long-run cost function?