1. Set up Ross’s challenge as a linear programming (LP) problem. Identify the critical decision variables, objective function, and constraints.

2. What is the optimal combination of drinks that Ross must sell to maximize his profits each week?

While attending college, Ross Tylman worked as a bartender at a local restaurant to pay his way through school. Far from finding the work tedious, he enjoyed the time he spent with the wait staff, customers, and the restaurant’s managers; so much so, in fact, that upon graduation, he decided that he wanted to open his own bar in that same college town. He secured funding from family members, friends, and a local bank and set out to make his fortune. Ross realizes that he owes money to his family and is determined to pay them back as quickly as possible.

Ross currently offers three drink options: beer, wine, and mixed drinks. Beer and wine are the easiest to serve in a short time but have the lowest profit margins. Mixed drinks take longer to make but have a higher profit margin. His cost per unit (bottle) for beer is $1.85; for a glass of wine, it is $2.50, and for mixed drinks, it is $3.00. He has $7,000 in cash available to purchase the beer, wine, and mixed drinks. Ross can serve one bottle of beer in 1 minute, a glass of wine in 2 minutes, and a mixed drink in 5 minutes. For each beer Ross sells, he can make $2.15; his unit profit for a glass of wine is $3.10, and each mixed drink earns him a profit of $4.25. His bar is open for 90 hours each week. To meet his financial obligations such as rent on the bar facilities and other interest payments, Ross has calculated that he has to sell at least 1,000 bottles of beer, 900 glasses of wine, and at least 500 mixed drinks per week.

Ross’s goal is to maximize his weekly profit. What is the best combination of drinks that will allow Ross to maximize profit from his bar’s sales?