Ace Lumber and Building Supply in Andover, Maryland, has received the following order for standard 1x12 boards to be cut in three lengths
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Order for 1x12 Boards
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Length
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Quantity
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7 ft
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700
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9 ft
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1200
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10 ft
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300
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The company maintains 1x12 boards in 25-foot standard-length in stock. Therefore, the 25-foot boards must be cut into the lengths necessary to meet the order requirements. The company wishes to minimize the number of standard-length boards used to satisfy this order.
a. Formulate a linear programming model that can be used to determine the minimum number of standard-length (25-foot) boards to cut in completing this order.
b. Determine the optimal solution including the total number of boards used.