Betty Malloy, owner of Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday, and she should determine how much beer to stock. Betty stocks 3 brands of beer - Yodel, Shotz, and Rainwater. The cost per gallon (to the tavern owner) of each brand is as follows:
The tavern has budget of $2,000 for beer for Super Bowl Sunday. Betty sells Yodel at the rate of $3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater at $1.75 per gallon. Based upon past football games, Betty has determined the maximum customer demand to be 400 gallons of Yodel, 500 gallons of Shotz, and 300 gallons of Rainwater. The tavern has the capacity to stock 1,000 gallons of beer; Betty wishes to stock up completely. Betty wants to find out the number of gallons of each brand of beer to order so as to maximize profit.
a. Formulate the linear programming model for this problem (written in the format similar to the way Problems 1 and 2 were presented).
b. Solve this problem using the computer.