Problem 21 A consumer consumes two (food) commodities, x and y. The consumer has utility function U(x,y) =log(x)+2log(y+2) The consumer seeks to maximize utility gained from consumption subject to four constraints. The amounts of x and y consumed must both be nonnegative. The consumer has 20 to spend. x sells for $2, y sells for $1. Finally, the consumer is on a diet requiring them to consume no more than 2000 calories. There are 150 calories in each unit of x and 200 calories in each unit of y. a) Write out the consumer's optimization problem and solve for the optimal consumption plan. b) What is the marginal utility of a calorie at the optima