IEOR 162, Fall 2011 Homework 10 1. (Problem 9.2.10; 5 points) If x and y are integers, how could you ensure that at least one of x + y ≤ 3 and 2 x + 5 y ≤ 12 is satisﬁed? 2. (Problem 9.2.11; 5 points) If x and y are integers, how could you ensure that whenever x ≤ 2 is satisﬁed, then y ≤ 3 is satisﬁed? Hint. The information that x is an integer is critical. 3. (Problem 9.2.12; 10 points) A company is considering opening warehouses in four cities: New York, Los Angeles, Chicago, and Atlanta. Each warehouse can ship 100 units per week. The weekly ﬁxed cost of keeping each warehouse open is $400 for New York, $500 for Los Angeles, $300 for Chicago, and $150 for Atlanta. Region 1 of the country requires 80 units per week, region 2 requires 70 units per week, and region 3 requires 40 units per week. The costs (including production and shipping costs) of sending one unit from a plant to a region are shown in the table below. From
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