Eagle Tavern Yodel Shotz Rainwater Cost Per Gallon 150905

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Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday, and she must determine how much beer to stock. Betty stocks three brands of beer—Yodel, Shotz, and Rainwater. The cost per gallon (to the tavern owner) of each brand is as follows: Brand Cost/Gallon Yodel $1.50, Shotz $0.90, Rainwater $0.50. The tavern has a budget of $2,000 for beer for Super Bowl Sunday.

Betty sells Yodel at $3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater at $1.75 per gallon. Based on past football games, Betty has the maximum customer demand of 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 and wants to stock completely. Betty aims to determine the values for the number of gallons of each brand to order to maximize profit.

Paper For Above instruction

The problem faced by Betty Malloy at Eagle Tavern involves selecting quantities of three beer brands—Yodel, Shotz, and Rainwater—to maximize profit while adhering to budget, demand, and capacity constraints. This scenario could be modeled as a linear programming problem that optimizes the profit function based on the number of gallons ordered for each brand, considering all constraints.

Let’s define the decision variables:

• Let x_Y = number of gallons of Yodel ordered
• Let x_S = number of gallons of Shotz ordered
• Let x_R = number of gallons of Rainwater ordered

The objective function to maximize is the profit, which is total revenue minus total cost. The revenue from each brand is its selling price multiplied by the number of gallons sold, and the cost is the cost per gallon multiplied by the number of gallons ordered. For the purpose of profit maximization:

Profit = (Selling price per gallon - Cost per gallon) * number of gallons

• Yodel profit per gallon = $3.00 - $1.50 = $1.50
• Shotz profit per gallon = $2.50 - $0.90 = $1.60
• Rainwater profit per gallon = $1.75 - $0.50 = $1.25

Therefore, the objective function becomes:

Maximize Z = 1.50 x_Y + 1.60 x_S + 1.25 x_R

Subject to the following constraints:

• Budget constraint: 1.50 x_Y + 0.90 x_S + 0.50 x_R ≤ 2000
• Demand constraints: x_Y ≤ 400; x_S ≤ 500; x_R ≤ 300
• Capacity constraint: x_Y + x_S + x_R ≤ 1000
• Non-negativity constraints: x_Y ≥ 0; x_S ≥ 0; x_R ≥ 0

This linear programming model can be solved via a computer optimization tool such as Excel Solver, R, or Python's linprog function. Solving the model provides the optimal quantities of each beer brand that maximize profit within the given constraints.

Implementing this LP, the solution would select the combination of beers that yields the maximum profit, subject to the constraints. For instance, the solution might suggest purchasing the maximum demand of the most profitable beer within the budget and capacity constraints, then allocating remaining capacity among the other beers to maximize total profit.

Such models are crucial in operational decision-making, ensuring minimum costs and maximum profitability in inventory stocking policies for taverns during high-demand events like the Super Bowl.

References

• Hillier, F. S., & Lieberman, G. J. (2015). Introduction to Operations Research (10th ed.). McGraw-Hill Education.