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The ACME Lock Company's production function is given by Q = 10K0

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The ACME Lock Company's production function is given by Q = 10K0.7L0.3, where K and L are ACME's annual capital and labor inputs, respectively, and Q is their annual output, measured in 1000s of locks. 

The prices per unit of capital and labor are pK = $10000 and pL = $5000, respectively. 

(a) (6 pts) Find ACME's minimum cost of producing 60,000 locks. 

(b) (2 pts) Find ACME's maximum output if their production budget is B = $100,000.

Hint: You can use information from (a) to help solve (b) ? you don't have to do the optimization problem from scratch (unless you want to).

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