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=3 for labor and capital respectively. It operates in a perfectly competitive environment facing a pricep=$48 , and uses an initial amount of capitalK^=12

.

Compute Kendall Square Inc's long-run cost function, calculate the long-run cost of producing 8 units of ramen.

Now suppose that, in addition to its existing capital and labor inputs, Kendall Square, Inc must hire a manager for a fixed amount of$54 in order to function properly. Suppose that all firms have the same long-run cost function as Kendall Square, Inc (they must also hire a similar manager), and the market demand is given byD(p)=9720p. . Suppose there are 59 other identical firms in the market (i.e. 60 identical firms in total) and no entry or exit due to government regulation.

What is the firm's profit?