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Find a combination of input factors that minimizes the following total cost: TC = 3L2 + 5LK + 7.5K2 - 20L - 21K + 44.2

Find a combination of input factors that minimizes the following total cost:

TC = 3L2 + 5LK + 7.5K2 - 20L - 21K + 44.2

Using the second order conditions prove that this combination corresponds to the minimum. What is the value of the minimum possible total cost?

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