Given the Production Function of a perfectly competitive firm: Q = 30L + 12L2 - 0.5L3 , where Q = Output and L = labor input

a. At what value of L will Diminishing Returns take effect?

b. Calculate the range of values for labor over which stages I, II, and III occur?

c. Suppose that the wage rate is $30 and the price of output is $2 per unit. How many workers should the firm hire?

d. At what value of L will Q be at its maximum? What is the maximum amount of Q?

e. If demand forecasts predict an output level of between 900 and 1100 in the next decade, what would be your long-run strategy to optimize the resources of your company?

Could I please have an explanation of the "why" behind each step, please? Thank you!