The production function for orange juice is:

Q = 60L - L²

Orange juice sells for $2 per unit.The cost of each unit of labor (L) is $20 per hour.

a.What is the optimal amount of labor (L) to hire?

b.If the company raises their price to $4, what would the optimal amount of (L) to hire?

c.Assume the workers unionize and increase the wage to $24 per hour (the price is back to $2).What would happen to the optimal amount of labor to hire?Explain.

d.Now the firm adds machines to its production process.The new production function is:

Q = 60L - L² + 90K - K²

Orange juice sells for $2 per unit.The cost of each unit of labor (L) is $20 per hour, and the cost of each unit of capital (K) is $30 per hour.

What of the two inputs is initially more productive?Explain.