VI. Solve the following problem max0Texp(t)[1exp(c(t))]dt such that k=k(t)c(t)k(t)k(0)=k0k(T)=b where c(t) and k(t) are the per-capita consumption and capital-labor ratio, respectively. [1exp(c(t))] is the utility of consumption, >0 is the rate of time preference, and is the depreciation rate of capital (>). The economic agent will choose how much to consume in order to maximize discounted utility from time 0 to time T. Once the optimal consumption path is determined, the capital path will be completely determined. VI. Solve the following problem max0Texp(t)[1exp(c(t))]dt such that k=k(t)c(t)k(t)k(0)=k0k(T)=b where c(t) and k(t) are the per-capita consumption and capital-labor ratio, respectively. [1exp(c(t))] is the utility of consumption, >0 is the rate of time preference, and is the depreciation rate of capital (>). The economic agent will choose how much to consume in order to maximize discounted utility from time 0 to time T. Once the optimal consumption path is determined, the capital path will be completely determined