The total monthly profit for NEST Controls in manufacturing and selling x hundreds of its standard thermostats and y hundreds of its deluxe thermostat each month is given by the total profit function: P(x, y) = - -x2 =y2 - -xy + 13x + 40y - 400 where P is in hundreds of dollars. If the production of thermostats is to be restricted to a total of exactly 5,000/month, how many of each model should NEST manufacture in order to maximize its monthly profits? What is the maximum monthly profit? (10 points)