Please show all your work, thank you!

4. Sonia likes ice skates and also likes going skating. Her utility function for pairs of ice skates, S, and the number of times she goes skating per month, T, is U(S,T) = 3ST , so MU s = 3T and MU T 2 3S . It costs Sonia $60 to buy a new pair of skates, or to spend the day at the skating rink. Assume that she has $600 to spend on skates and skating. a. What is the equation for her budget line? Draw it (with T on the vertical axis), and label the slope and intercepts. b. What is Sonia's marginal rate of substitution? Explain. c. Solve mathematically for her optimal bundle. Show how to determine this bundle in a diagram using indifference curves and a budget line