Problem 2 Hard Rock Cafe's is considering opening several new restaurants in Canada and has identified...

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Problem 2 Hard Rock Cafe's is considering opening several new restaurants in Canada and has identified 5 possible locations with estimated annual profit and construction cost in million. Also shown is the size of the restaurant that can be constructed at that location (in 1000 sqft). Hard Rock has budgeted $22 million dollars to spend in construction cost. It also wants to have total capacity to be at least 20,000. Locations 1 2 3 4 5 Estimated annual profits Construction cost 16 22 10 8 15 7 12 4 3 6 Capacity 10 15 7 5 9 (a) Formulate an IP whose solution will tell Hard Rock where it should build the new restaurants to maximize annual profits. Solve the model using LINGO. Which location should Hard Rock choose to open a restaurant and what is the estimated annual profit? (8 marks) (b) What constraint(s) will you need to add for following? (1) if a restaurant is opened at location 3, then one will be opened at location 5 also. (1 marks) (2) a restaurant could be opened at location 1 only if a restaurant is opened at location 4. (1 marks) (3) A restaurant must be opened at location 2 if one is opened at either location 3 or 4. (2 marks) (4) A restaurant must be opened at location 2 if one is opened at both locations 3 and 4. (2 marks) Problem 2 Hard Rock Cafe's is considering opening several new restaurants in Canada and has identified 5 possible locations with estimated annual profit and construction cost in million. Also shown is the size of the restaurant that can be constructed at that location (in 1000 sqft). Hard Rock has budgeted $22 million dollars to spend in construction cost. It also wants to have total capacity to be at least 20,000. Locations 1 2 3 4 5 Estimated annual profits Construction cost 16 22 10 8 15 7 12 4 3 6 Capacity 10 15 7 5 9 (a) Formulate an IP whose solution will tell Hard Rock where it should build the new restaurants to maximize annual profits. Solve the model using LINGO. Which location should Hard Rock choose to open a restaurant and what is the estimated annual profit? (8 marks) (b) What constraint(s) will you need to add for following? (1) if a restaurant is opened at location 3, then one will be opened at location 5 also. (1 marks) (2) a restaurant could be opened at location 1 only if a restaurant is opened at location 4. (1 marks) (3) A restaurant must be opened at location 2 if one is opened at either location 3 or 4. (2 marks) (4) A restaurant must be opened at location 2 if one is opened at both locations 3 and 4. (2 marks)