how we got the underlined answer of below questions (mathematically) in details:

1-

Flath (2011) estimated that the Cobb-Douglas production function of a typical Japanese beer manufacturer.

-The production function is Q = 1.52L0.6K0.4.

-Assume that firm's capital is fixed at K = 100 units in the short run, the rental rate is r = $8, and the wage is w = $24.

-

Calculating cost curves:

-Q = 1.52L0.6(100)0.4, implying L 0.023Q1.67

2-

Given the production function Q = 4L + K, what is the marginal product of labor when capital is fixed at 50?

a.1

b.4

c.50

d.54

e.250

3-

Suppose the short-run production function is Q = 10L. If the wage rate is w = $10 per unit of labor, then AVC equals

a.Q

b.Q/10

c.1

d.1/Q

e.10/Q