2) Smelly Industries is considering expaning into British Columbia. This expansion would create facilities for the production of Santa's Beard Scented Candles. In total Smelly Industries estimates that they need a capacity of 450,000 units per year and needs to have an operating cost for the production facilities below $7.5 million per year. The selection committee has narrowed the list two four possible locations: Surrey, Coquit- lam, Abbotsford, or Chilliwack. Smelly's management has established a construction cost limit of $45 million for the expansion. This money will be used to build some combination of plants that provides the maximum yearly profit. The Surrey location can have one of three different-sized plants built, but the other three locations have no flexibility with the size of the plant due to zoning laws. The table below gives an estimate of the production capacity, yearly operating cost, yearly profit, and overall construction cost. Plant Production Operation Yearly Construction Site Capacity Cost Profit Cost Location (units/yr.) ($/yr.) ($/yr.) ($) Surrey Size 1 250,000 4,000,000 400,000 25,000,000 Size 2 225,000 3,500,000 350,000 22,000,000 Size 3 200,000 3,000,000 300,000 19,000,000 Coquitlam 200,000 3,000,000 325,000 22,000,000 Abbotsford 225,000 3,000,000 275,000 23,000,000 Chilliwack 200,000 2,500,000 325,000 20,000,000 (a) Show the linear programming problem. (b) Which sites should be selected? If Surrey is selected, make sure to indicate which size plant should be constructed. (c) Suppose that the company is considering running two warehouses (one in Langley and one in Richmond). The demand in Langley is 300,000 units, while Richmond only require 150,000 units. If the cost of per unit delivery is shown in the table below, are the same decisions made as in part (b)? How do the profits compare? Langley Richmond Surrey Coquitlam - 09 Abbotsford Chilliwack

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