Question 1. Suppose a company producing hand sanitizer has the following production function q=f(K, L)=2K+L0.5 , where K is capital and L is labor.

a) Calculate marginal product of capital (MPK) and marginal product of labor (MPL) when K=1 and L=4.

b) Compute marginal rate of technical substitution (RTS) for this production function when K=1 and L=4. Assume L is on the horizontal axis.

c) Does this production function exhibit increasing return to scale, decreasing return to scale or constant return to scale? Prove your answer.

d) Suppose w=$0.5 (wage of labor) and r=$2 (rental price of capital), calculate the K and L that will produce 100 hand sanitizers in the least costly way.

e) What is the minimized total cost in part d) when the company produces 100 hand sanitizers in the least costly way?