A competitive firm uses three factors of production. Its production function is a = f(x, y, z) = (2x + y)^(1/2)z^(1/2).

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A competitive firm uses three factors of production. Its
production function is a = f(x, y, z) = (2x + y)^(1/2)z^(1/2). The
input prices are Wx = $1, Wy = $2, and Wz = $3.
a. Does this firm have increasing, decreasing, or constant returns
to scale? Show.
b. The firm wants to make 100 units of a. What inputs should it
choose? Find the general cost function given the input
prices.
c. If the input price of y is reduced to $0.5, what happens to
production costs? Explain.