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 Hardgraves 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: From:	Hamilton	Regina
Kingston Prince George	$30 $45	$40 $66
Sudbury Abbotsford	$38 $30	$27 $50

Hardgrave estimates that the monthly fixed cost of operating the proposed facility in Sudbury would be $400,000. The Abbotsford plant would be somewhat cheaper due to the cheaper cost of living at that location. Hardgrave therefore estimates the monthly fixed cost of operating the proposed facility in Abbotsford would be $325,000. Note that the fixed costs at existing plants (i.e., plants in Kingston and Prince George) need not be considered since they will be incurred regardless of which plant Hardgrave decides to open.

Formulate algebraically the above problem to help Hardgrave decide which one of the new locations, Sudbury OR Abbotsford, will yield to the lowest production and transportation costs in combination with the existing plants and warehouses. DO NOT SOLVE.