QUESTION 2: Transportation + Binary Integer Programming Application (25 points)

QUESTION 2: Transportation + Binary Integer Programming Application (25 points) The Hardgrave Machine Company produces computer components at its plants in Kingston, ON and Prince George, BC. These plants have not been able to keep up with demand for orders at Hardgrave's two warehouses in Hamilton and Regina. The firm has therefore decided to build ONE new plant to expand its productive capacity. The two sites being considered are Sudbury, ON and Abbotsford, BC. The tables below present the information of: (i) the production cost and capacity for each of the two existing plants; (ii) demand at each of the two warehouses; and (iii) estimated production costs for the new proposed plants. Production Plant |Monthly Supply (units) |Production Cost per Unit ($) Kingston 15,000 $50 Prince George 20,000 $52 Total 35,000 units Warehouse Monthly Demand (Units) Hamilton 30,000 Regina 25,000 Total 55,000 units Supply needed from new plant = 55,000 - 35,000 = 20,000 units per month New Plant Estimated Production Cost per Unit at Proposed Plants Sudbury $53 Abbotsford $49 Transportation costs per unit from each plant to each warehouse are summarized in the following table: To: Hamilton Regina From: Kingston $30 $40 Prince George $45 $66 Sudbury $38 $27 Abbotsford $30 $50