Hernandez Corp. uses two variable inputs, X and Y, to produce its final product, canoes. Its engineering department has estimated the marginal product functions for inputs X and Y as follows: MPx = Y/X MPy = 4 X/Y Where X and Y denote, respectively, the quantity in hours of inputs X and Y used. At present Hernandez Corp. pays $40 per hour for input X and $10 per hour for input Y. It is using 200 hours of X and 100 hours of Y per day.
a. Write a paragraph explaining how the Hernandez Corp. finds the least cost combination of inputs for producing a given rate of output.
b. Using the data provided above, determine if the Hernandez Corp. is using a cost minimizing combination of inputs. Explain your answer/show your work. If your answer is no, how should the input combination be adjusted?