Problem 20 A consumer consumes two foods x, and y. The consumer has utility function Ux,y) =4xy 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 $24 to spend. Each unit of x sells for $2, each unit of y sells for $1. Finally, the consumer is on a diet requiring them to consume at least 2500 calories. There are 200 calories in each unit of x and 100 calories in each unit of y. 3) Write out the consumer's optimization problem and solve for the optimal consumption plan, if it exists. c) What is the marginal utility of a calorie at the optima, if it exists