Suppose the process of producing lightweight parkas by Polly’s Parkas is described by the function:
q = 40K0.6 (L-40)0.4
where q is the number of parkas produced, K the number of computerized stitching-machine hours, and L the number of person-hours of labor. In addition to capital and labor, $10 worth of raw materials is used in the production of each parka.
Note that əq/əK = 40(0.6) K -0.40 (L-40)0.4 and əq/əL = 40K 0.6 (0.4) (L-40) -0.60
By minimizing cost subject to the production function, derive the cost-minimizing demands for K and L as a function of output (q), wage rates (w), and rental rates of machines (r).
The cost-minimizing demands for K and L are:A. K=0.020q (r/w)0.6 + 40 and L=0.020q (r/w)0.6 = 40
B. K=0.030q (w/r)0.4 and L=0.030 (w/r)0.4
C. K=0.020q (r/w)0.6 + 40 and L= 0.030q (w/r)0.4
D. K = 0.030q (w/r)0.4 and L = 0.020q (r/w)0.6 + 40
E. none of the above