Suppose a plant mass-produces engines by teams of worke

Suppose a plant mass-produces engines by teams of workers using as-
sembly machines. The technology is summarized by the production function
q = 3K^0.5 L^0.5
where q is the number of engines per week K is the number of assembly
machines and L is the number of labor teams. Each assembly machine rents
for r = $9000 per week and each team costs w = $4000 per week. Engine
costs are given by the cost of labor teams and machines.
Suppose the plant is cost minimizing.
What is the cost function for the plant
How much would it cost to produce q engines?
What are average and marginal costs for producing q engines?
What is the cost minimizing input combination of producing q =
1800?
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