The Smith Family’s utility function is given by U = 7 ln x + 13 ln y,
Where U is their monthly utility, x is the quantity of essential goods that they consume per month and y is the quantity of luxury goods that they consume per month. The average price per unit of essential goods is px = $10 and the average cost per unit of luxury goods is py = $30. Find the quantities of essential and luxury goods that the Smith family should consume per month to maximize their utility, given that their monthly budget for these goods is B = $3600. What is their maximum utility? Be sure to justify your claim that the utility you find is the absolute maximum.