solve it within 30 minute

Problem 4 (10 points) A chemicals firm is planning for an increase of product capacity. They have estimated that the cost of adding new capacity obeys the law F(y) =0.0125 y0.60 Where cost is measured in millions of dollars and capacity is measured in tons per year. The demand is growing at 4,000 ton per year. Future costs are discounted using 15% per year. a) Determine the optimal timing of plant additions and the optimal size of each addition. b) the optimal size of each addition c) What is the cost of each added capacity