Q1. A Japanese steel manufacturer is considering expanding operations. From experience, it estimates that new capacity addition obey the law \mathrm{f}(\mathrm{y})=0.00345 y^{0.51} Where the cost, f(y), is measured in millions

of dollars and y is measured in tons f steel produced. If the demand for steel is assumed to grow at the constant rate of 8,000 tons per year. Assume that annual interest rate is 10 percent. What is the optimal number of years between new plants opening and optimal value of plant capacity? (15 points)