Tim consumes a diet of cheesecake (C) and Sprite (S). The utility function for Tim is U(C, S) = 8CS. The price of a cheesecake (PC) is $4 and the price of a Sprite (P_S) is $2. Tim's income (M) is $800. Assume that cheesecake (C) is measured on the horizontal axis and Sprite (S) is measured on the vertical axis.

a. Obtain the MU_Cand MU_S.

b. Set up the condition for calculating the consumer equilibrium levels of cheesecake (C) and Sprite (S) to consume.

c. Write the equation for the budget line. Make sure to substitute in the numerical values provided.

d. Calculate the consumer equilibrium levels of cheesecake (C) and Sprite (S) that maximize Tim's utility subject to the budget line.