Tianyu has a $10 budget for his breakfast at his favorite coffee shop. The menu has two items: coffee is $5 per cup and croissants are $2.5 per each. The coffee shop has a special promotion for coffee: if you purchase two cups of coffee, you will get the third cup for free (buy-two-get-one-free). Tianyu's preference over coffee (good x) and croissants (good y) can be represented by a utility function u(x, y) = In x + In y where MUX = and MU = y E. (10 points) The coffee shop now offers a new product, chocolate muffins, at a price of $3 per each. Tianyu's preference over croissants (good x) and muffins (good z) can be represented by a utility function v(x, z) = x + z, so his breakfast utility function (with coffee, good y, included) can be rewritten as u(x, y, z) = ln(x + z) + Iny where MUx = MUZ MUy 1 = and x+z = How will Tianyu adjust his breakfast purchase? Explain your answers carefully. y Optimal coffee consumption: Optimal croissant consumption: Optimal chocolate muffin consumption: Your explanation here: