A company considers opening distribution centers in (1) New Brunswick, (2) Waterloo, (3) Montreal, (4) Ottawa, and (5) Toronto. The cost of building the five terminals (in millions of dollars) would be 10 in New Brunswick, 14 in Waterloo, 18 in Montreal, 17 in Ottawa, and 24 in Toronto. No more than two terminals may be built. If a terminal is built in Ottawa, then one must be built in New Brunswick. At least one terminal must be built in Montreal, Ottawa, or Toronto. a) Formulate this location problem as an integer problem (i. e. define the variables and write down the objective function and all constraints in algebraic form).
b) Create a spreadsheet model for this problem and solve it with Solver.
c) What is the optimal solution? What is the optimal value?
d) How much would the company save without this requirement: "If a terminal is built in Ottawa, then one must be built in New Brunswick"?