An agricultural experiment examined the response of corn production (output C) to variations in two inputs pounds of nitrogen fertilizer per acre (N) and the number of corn plants planted per acre (P). Thus, the production function is on the form C = f(N,P). The results of this experiment are presented below, where the numbers in the matrix are the bushels of corn yielded per acre (output C) resulting from the various combinations of the inputs N (rows in the matrix) and P (columns in the matrix)
lbs of Nitrogen (Per acre (N) #of plants placed per acre(P)
9000 12000 15000 18000
0 50.6 54.2 53.5 48.5
50 78.7 85.9 88.8 87.5
100 94.4 105.3 111.9 114.2
150 97.8 112.4 122.6 128.6
does the law of diminishing returns hold in this case when the # of pounds of nitrogen per acre (N) is considered to be the variable input? give a numerical example.