A local brewery produces three types of beer: premium, regular, and light. The brewery has enough vat capacity to produce 27,000 gallons of beer per month. A gallon of premium beer requires 4.3 pounds of grain, a gallon of regular requires 3.8 pounds of grain, and a gallon of light requires 3.5 pounds of grain. The brewery is able to acquire 45,000 pounds of grain every month. Although the brewery's largest seller is regular beer, it wants to have a competitive market mix of beer. Thus, the brewery wishes to produce at least 4000 gallons each of light beer and premium beer, but not more than 12,000 gallons of these two beers combined. The brewery makes a profit of $3.00 per gallon on premium beer, $2.40 per gallon on regular beer, and $2.80 per gallon on light beer. The brewery manager wants to know how much of each type of beer to produce to maximize profit.

Formulate a linear programming model for this problem.