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Question 2: (11 marks) (For this question you may use pages to write the expressions or formulas and upload the acceptable image files for faster response) The Assiniboine Manufacturing Inc. (AMI) operates a production facility in North York with production capacity of 20,500 units. All finished products of AMI will be directly shipped to their customers. The customers of AMI are in Hamilton, St. Catherine's and Waterloo areas. Because of an increasing demand from customers, AMI plans to increase the production capacity by constructing new production facility in one or more of the following cities: Etobicoke, Newmarket, Markham and Orillia. If AMI has $900,000 as available capital for new facility constructions; the estimated construction cost and production capacity for the four proposed facilities are as follows: Proposed Facility Construction Cost Production Capacity (Units) Etobicoke $305,000 13,500 Newmarket $315,000 14,000 Markham $275,000 21,500 Orillia $180,000 27,000 According to the marketing survey, the anticipated demands of customers in different areas are: Hamilton = 18,000 units, St. Catharine's = 11,500 units and Waterloo = 24,500 units The shipping costs per unit among different locations are provided as below: Hamilton St. Catharines Waterloo Facility in Etobicoke $4 $6 $13 Facility in Newmarket $7 $8 $12 Facility in Markham $10 $13 $15 Facility in Orillia $17 $15 $11 Facility in North York $2 $7 $14Suppose you are the logistics manager of AMI and your task is to formulate this problem as a linear programming model by choosing the best production facilities and meeting the anticipated demand from customers with the minimum total costs. (For this question you may use pages to write the expressions or formulas and upload the acceptable image files for faster response) 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 righthand side of constraints. d] Write a constraint to ensure at least 3 proposed facilities can be constructed by AMI. e) Write the constraint showing that facility construction in Newmarket is the conditional on the facility construction in Markham, and vice versa