optimization problem

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Question: You work for a company in the food sector and management asked you to find the best spots to place...

You work for a company in the food sector and management asked you to find the best spots to place restaurants in a new area. This new area contains several neighborhoods (black icons in the figure below). A restaurant can be placed on any square, white or black, in the grid below and it will service nine squares (the eight squares surrounding its location plus that of its own location). Management admits that it might not be of financial interest to service all neighborhoods, so they will be happy as long as 70% of them are covered. Since restaurants are an important investment, management urges you to service this 70% with the least possible number of restaurants.

(a) Write this problem as an optimization problem.

(b) Solve it with Excel.