PLEASE SHOW ALL WORKING

Q4: (20 points) Evelin wants to exercise and have choices of going to a Yoga class and/or a Zumba class. Each Yoga class costs $2 and each Zumba class costs $1. The following utility function reflects Evelin's preferences: U(y,z) = y'z+ 4y? where y is the number of Yoga classes per semester and z is the number of Zumba classes per semester. Evelin's budget for exercising is $80 per semester. Please answer the following questions. 1. What is Evelin's budget constraint? Express the constraint as a function of z (e.g., f(z)). Draw the budget line. Compute the MRT and explain the economic meaning of it. If she takes 24 Yoga classes and 40 Zumba classes, can she afford all these classes? 2. Write down Evelin's MRS of Yoga class and Zumba class. Explain the economic meaning of her MRS. Compute her MRS when she takes 24 Yoga classes and 40 Zumba classes. State in words what the value of the MRS means. 3. Please find the number of Yoga classes and the number of Zumba classes (y and z) that will make her most happy given her budget of $80. (write down Evelin's optimization problem and show your calculation step by step.) 4. For some reason, Evelin's budget has been cut to $40. At the same time, the price for each Zumba class has increased to $6. The price for each Yoga class has not changed. Please find Evelin's optimal choice of the Yoga and Zumba classes