Suppose the production function is p(x, y) = .5 .52 (x + y), the price of good x is $4, the price of good y is $1, and the price of the output is $10. What values for x and y will maximize the profit given this information. Also, solve for whether there is diminishing marginal product with respect to each of the inputs and whether there is diminishing technical rate of substitution for this production function.