Suppose Zeta company has the following short-run production function, where Q is output  per time period and L is the number of units of labor hired

Suppose Zeta company has the following short-run production function, where Q is output  per time period and L is the number of units of labor hired.

                 Q = -(1/3)L³ + 4L² + 20L

     a) What will be L and Q at the maximum short-run output (Q)?

     b)  What will be L and MP_L at the maximum MP_L?

    c)  At what level of output will the firm reach the point of diminishing returns to L?

    d)  Find L, AP_L and MP_L at the maximum AP_L.

  e)  Determine the boundaries of the three stages of production (i.e., Stage 1, Stage 2, and

       Stage 3) in terms of L.