Please show your work and make sure your answers are correct.

Suppose that soccer balls are produced using labor (L) and capital (K) according to the following production function: 1 3 e = 12LK where Q is the number of balls being produced. The wage is $30 and the rental rate is $10. a) The owner of a soccer balls factory has decided to enter a new regional market. Assuming transportation costs are zero, is it more efficient for the owner to open a new plant in the target regional market or produce both markets' outputs in its current plant? Does it matter which of these two options the owner chooses? Explain your answer in detail