Before the completion of the R & D program, the technology of the firm is represented by the follow- ing production function: Y = AF[K], 0 st 0 is the rise in productivity, and K, is the capi- tal stock at time t, tz T. The problem faced by the firm is to find an investment program (l)o to maximize the fhe present value of the stream of profits associated with an investment program. Formally, this problem can be stated as follows: viko. 0] = max(AF[K] -4 -x)dt + ((A+AA) F[KJ-I-x)dt subject to = I, Ko is given. Herer is the interest rate. Note that in the problem just stated the capital stock cannot be adjusted instantaneously without incurring prohibitive adjustment costs. More precisely, if I, is the amount of capital invested (or dis-invested), then the total cost of investment is given by + where x is a positive constant. Explain how the investment problem of the firm can be solved. In answering this question, it is not necessary to provide a complete solution to the problem.