Tony Hawk's Birdhouse Skateboards produces skateboards (y) using essentially two types of inputs: decks (x₁) and wheels (x₂). The production function is y = min{x₁,4x₂}. It's not technically a skateboard if it has less than four wheels, and you can have a double-decker, but it is still considered one skateboard, if it only has four wheels.

a)Tony Hawk has 1,000 decks and 4,000 wheels. How many skateboards can he produce?

b)Given the production point of part a, what is the marginal product of adding an additional wheel (while keeping x₁ fixed)?

c)Suppose Tony Hawk has 1,001 decks and 4,003 wheels. Does your answer in part a change? What is the marginal product of adding an additional wheel now?

d)Back to the production point of part a, what is the Technical Rate of Substitution?

e)If Tony Hawk doubles his inputs, does the quantity of skateboards he can produce double, more than double or less than double?