Here we will look at a multi-period dynamic optimization problem: a cake-eating example. Suppose that you are presented with a cake of size W. At each time period, t = 0, 1, 2, ..., T-1, you can eat some of the cake but must save the rest. Let ct be your consumption in period t, and let u(ct) = act - bc represent the flow of utility from this consumption. We could represent your lifetime utility by T-1 u(c)/(1+8)t t=0 Now assume W = 12, T = 7, a = 6, and b = 0.2. The discount rate is 5%. Set up your utility maximization problem and find the optimal path of consumption.