The first question is free response, the second is multiple choice and the third is free response. For the multiple choice, the options are listed right below the question. Thanks!

1) Imagine there are two goods, H and S. The utility function is: U = H^1/2S^1/2.The price of H is $6 and the price of S is $3.The budget is $18.What is the optimal quantity of H to consume?

2) Emily's and Lavander's preferences about yogurt and protein bars are possibly different. Both are well-behaved, though. Also, the two girls have the same budget. The price of the cup of yogurt is $1 and each protein bar costs $2. Knowing Emily's optimal bundle is 8.2 cups of yogurt and 4.25 protein bars, which of the options below could be Lavander's optimal bundle?

a. 7.2 cups of yogurt and 6.25 protein bars

b. 10 cups of yogurt and 6.7 protein bars

c. 15 cups of yogurt and 0.85 protein bars

d. 4.1 cups of yogurt and 8.5 protein bars

3) Gennaro's preferences can be represented by the utility function U = X²Y². His budget is $60, price of good X is $3, price of good Y is $4. What is his level of utility when he consumes his optimal bundle?