A person's utility function (U) is given by the following expression:
U(x,y) = (x + 2)(y + 1),
where x and y are products the consumer may purchase. Suppose that the price of x is $2.00 and the price of y is $5.00, and the consumer wants to spend exactly $51.00 on both products. The consumer's objective is to maximize her utility function subject to the stated budget constraint.
a. Write the LaGrange function for this problem.
b. Derive the optimal purchases for x and y. Show your work.
c. Verify whether the SOC for a maximum is satisfied. Show your work.