A firm produces two goods A and B. The weekly cost of producing x items of A

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A firm produces two goods A and B. The weekly cost of producing x items of A and y items of B is
TC = 0.2x2 + 0.05y2 + 0.1xy + 2x + 5y + 1000
(a) State the minimum value of TC in the case when there are no constraints.
(b) Find the minimum value of TC when the firm is committed to producing 500 goods of either type in total.

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