A dog breeder decides to feed his dogs a combination of two dog foods: Pixie Power and Misty Might. He wants the dogs to receive four nutritional factors each month. The amounts of these factors (a, b, c, and d) contained in 1 bag of each dog food are shown in the following chart, together with the total amounts needed.

The costs per bag are $50 for Pixie Power and $40 for Misty Might. How many bags of each dog food should be blended to meet the nutritional requirements at the lowest cost? Set this up as a linear programming problem in the following form: Minimize c^Tx subject to Ax ≥ b and x ≥ 0. Do not find the solution.

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Pixie Power Misty Might Needed a 3 نیا 2 28 b 2 4 30 с 1 3 20 d 2 1 25