Atkinson Manufacturing Inc. (AMI) operates a production facility in Vaughan with a production capacity of 22,500 units. All finished products of AMI will be shipped to the regional distribution centers located in Mississauga and Brampton before they reach the customers. The customers of AMI are in Milton, Guelph, and Kitchener areas.

Because of an increase in demand from customers, AMI plans to increase the production capacity by constructing a new production facility in one or more of the following cities: North York, Richmond, Markham, and Barrie. The estimated construction cost and production capacity for the four proposed facilities are as follows:

Proposed Facility	Construction Cost	Production Capacity (Units)
North York	$315,000	12,500
Richmond	$305,000	15,000
Markham	$295,000	21,000
Barrie	$160,000	27,500

According to the marketing survey, the anticipated demands of customers in different cities are Milton = 17,000 units, Guelph = 12,500 units and Kitchener = 23,500 units

The shipping costs per unit among different locations are provided as below:

	Distribution Center in Mississauga	Distribution Center in Brampton
Facility in North York	$5	$6
Facility in Richmond	$7	$8
Facility in Markham	$12	$9
Facility in Barrie	$17	$15
Facility in Vaughan	$4	$3

	Milton	Guelph	Kitchener
Distribution Center in Mississauga	$2	$10	$14
Distribution Center in Brampton	$5	$8	$13

Your task is to formulate the problem as a linear programming model by choosing the best production facilities and meeting the anticipated demand from customers with the minimum total costs.

a) Clearly define all decision variables

b) Clearly formulate the objective function

c) Clearly specify all the constraints such that only constants appear on the right-hand side of constraints.

d) Write a single constraint showing that if AMI is constructing a facility in either North York or Markham, then AMI must construct both of them.

e) Write a single constraint showing that if AMI is constructing the facility in Markham or Barrie, then AMI must also construct the facility in North York.

f) Write a single constraint showing that if AMI is constructing a facility in Barrie, then AMI must also construct the facility in North York, Richmond and Markham.