Formulate but do not solve the following exercise as a linear programming problem. Madison Finance has a total of $20 million earmarked for homeowner loans and auto loans, where x is homeowner loans in millions of dollars and y is auto loans in millions of dollars. On the average, homeowner loans have a 9% annual rate of return, whereas auto loans yield a 12% annual rate of return. Management has also stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the total amount of automobile loans. Determine the total amount of loans of each type Madison should extend to each category to maximize its returns P in millions of dollars. Maximize P = subject to the constraints total loans distribution of loans x 20 y 20