Alice 1 receives an allowance of 150 dollars a week for fish (which is an important share of her diet) that she spends on buying Salmon (S) and Tuna (T). The price of each pound of Salmon is 10 dollars and the price of each pound of Tuna is 5 dollars. Her utility is given by:

U(S,T)=S^1/2 + T^1/2

(a) Find her marginal rate of substitution (MRS) between S and T.

(b) Write down Alice's budget constraint.

(c) Find Alice's optimal consumption and the value of at the optimum

(d) What is her new consumption if the price of tuna becomes 10 dollars?