6.1. A firm uses the inputs of fertilizer, labor, and hot-houses to produce roses. Suppose that when the quantity of labor and hothouses is fixed, the relationship between the quantity of fertilizer and the number of roses produced is given by the following table: Tons of Fertilizer per Month Number of Roses per Month o o 500 1,000 1,700 2,200 2,500 2,600 2,500 2,000 0N oA~ WN a. What is the average product of fertilizer when 4 tons are used? b. What is the marginal product of the sixth ton of fertilizer? c. Does this total product function exhibit diminishing marginal returns? If so, over what quantities of fertilizer do they occur? d. Does this total product function exhibit diminishing total returns? If so, over what quantities of fertilizer do they occur? 6.2. A firm is required to produce 100 units of output using quantities of labor and capital (L, K) = (7, 6). For each of the following production functions, state whether it is possible to produce the required output with the given input combination. If it is possible, state whether the input combination is technically efficient or inefficient. a.Q=7L+8K b.Q = 20VKL . Q = min(16L, 20K) d.Q=2(KL+L+1) 6.4. Suppose that the production function for DVDs is given by Q = KL? L3, where Q is the number of disks produced per year, K is machine-hours of capital, and L is man-hours of labor. a. Suppose K = 600. Find the total product function and graph it over the range L = 0 to L = 500. Then sketch the graphs of the average and marginal product functions. At what level of labor L does the average product curve appear to reach its maximum? At what level does the marginal product curve appear to reach its maximum? b. Replicate the analysis in part (a) for the case in which K = 1,200. c. When either K = 600 or K = 1,200, does the total product function have a region of increasing marginal returns