What is the minimum cost for the objective function C=45⁢x+53⁢y if the vertices of a feasible region are at (0,9) , (12,8) , (20,9) , and (9,0) ?

Evaluate C = 45x + 53y at each vertex. The costs are 477 at (0, 9), 964 at (12, 8), 1,377 at (20, 9), and 405 at (9, 0). The smallest cost is 405, so the minimum occurs at (9, 0), choice D.

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