During each 4-hour period, the Smalltown police force requires the following number of on-duty police officers: 12midnight to 4 A.M.—8; 4 to 8 A.M.—7; 8 A.M. to 12 noon—6; 12 noon to 4 P.M.—6; 4 to 8 P.M.—5; 8 P.M. to 12midnight—4. Each police officer works two consecutive 4-hour shifts. Formulate an LP that can be used to minimize the number of police officers needed to meet Smalltown’s daily requirements.   Please solve the following problem as a linear program.

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Optimization Models

Optimization models are mathematical models that help organizations determine the best way to allocate scarce resources to achieve specific objectives. These models can be used to solve a wide variety of problems, from finding the most efficient route for a delivery truck to determining the optimal mix of products to stock in a store.