A firm's production function requires it to use workers in a fixed ratio to machines of 2 to 1. To produce 1 unit of output, the firm needs a minimum of 4 units of L and 2 units of K. These proportions hold for any level of output. Suppose the price of K (r) is $1 and the price of L (w) is $3. If both L and K are variable inputs, calculate the firm's TC and AC functions.

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