Assume Canon's production function for digital cameras is given by Q = 100(L 0.7K 0.3), where L and K are the number of workers and machines employed in a month, respectively, and Q is the monthly output. Moreover, assume the monthly wage per worker is $3,000 and the monthly rental rate per machine is $2,000. (Note: Given the production function, the marginal product functions are MPL = 70(L-0.3K 0.3 ) and MPK = 30(L 0.7K-0.7 )).
a. If Canon needs to supply 60,000 units of cameras per month, how many workers and machines should it optimally employ?
b. What are the total cost and average cost of producing the quantity given in (a)?