Determine the best monthly production schedule to meet delivery contracts and minimize total costs.

Premier Paints supplies to major contractors. One of their contracts for a specialty paint requires them to supply 750, 500, 400, and 950 gallons over the next 4 months. To produce this paint requires a shutdown and cleaning of one of their manufacturing departments at a cost of $1,000. The entire contract requirement can be produced during the first month in one production run; however, the inventory that must be held until delivery costs $0.75 per gallon per month. If the paint is produced in other months, then the cleaning costs are incurred during each month of production. Formulate and solve an integer optimization model to determine the best monthly production schedule to meet delivery contracts and minimize total costs.

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