Optimal Inputs

Consider a firm that uses labor (L) and capital (K) to produce a general output (q) using the following production function:

q = K ^1/4 L ^3/4

The firm seeks to produce q = 100 units for sale and faces prices for labor of w = 2 and capital of r = 6.

a) What is the marginal rate of technical substitution?

b) What are the optimal amounts of each input used by the firm? Round to three decimal places.

c) How much does the firm spend?