Reference no: EM132287496

Linear Programming:

Suppose a craft brewery has a monthly capacity of 50,000 barrels of beer and produces two styles of beer, a pale ale and a porter. The brewery cannot exceed the monthly capacity. At a craft brewery, four different ingredients are combined to create beer. Yeast, malted grain, hops and water are mixed, cooked, and fermented in large kettles. Production is also limited by the availability of grain, the capacity to ship grain to the brewery, and the storage capacity at the brewery. The brewery can process and store 4,000,000 pounds of malted grain per month. For each barrel of pale ale, the brewery uses 69.75 pounds of malted grain. For each barrel of porter, the brewery uses 85.25 pounds of malted grain. Hops are also used to make the pale ale and porter styles of beer. Each barrel of pale ale requires 23.8 ounces of hops. Each barrel of porter requires 10.85 ounces of hops. The brewery is able to acquire 62,500 pounds of hops each month. Suppose that each barrel of pale ale yields $100 of profit and each barrel of porter yields $80 of profit. Draw the feasible region and find the maximum profit for the brewery.