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?