Please help with this problem. I need help on all parts.

Problem 2: "To shop, or not to shop" A consumer has preferences described by the utility function u(c, q) = Inc + aq, where c denotes "necessity" consumption (food), q E {0, 1} denotes "luxury" consumption (cars), and a > 0 is a parameter. Cars are an indivisible good, so that you either buy it, or you do not. The price of food is equal to 1, whereas the price of a car is p. The consumer has income w. A. Solve for the optimal demand of food c* and cars q*. B. Introduce a proportional tax on the purchase of cars, To, so that the price of a car becomes p = (1 + T,)p. Obtain the new demand curve for cars. How does the demand for cars change when we increase To? Explain