Betty Malloy, Owner Of The Eagle Tavern In Pittsburgh

Question

Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday and needs to determine how much beer to stock. The tavern stocks three brands of beer—Yodel, Shotz, and Rainwater—each with different costs, selling prices, and demand limitations. The cost per gallon for each brand is: Yodel at $1.50, Shotz at $0.90, and Rainwater at $0.50. The selling prices are $3.00 for Yodel, $2.50 for Shotz, and $1.75 for Rainwater. The maximum customer demand based on past football games is 400 gallons of Yodel, 500 gallons of Shotz, and 300 gallons of Rainwater. The total beer stock capacity is 1,000 gallons, and Betty aims to fully stock her inventory. The goal is to determine the optimal quantities of each beer brand to order to maximize profit within the constraints of budget, capacity, and demand. This problem can be formulated as a linear programming model with decision variables representing the quantities of each beer to stock, an objective function to maximize profit, and constraints reflecting the costs, capacity, and demand limits.

Dr. Jack HW Helper · Accepted Answer

The problem faced by Betty Malloy in stocking beer for the Super Bowl Sunday at her tavern can be effectively modeled using linear programming. The primary goal is to maximize profit by deciding the optimal quantities of three different beer brands—Yodel, Shotz, and Rainwater—while adhering to budget, capacity, and demand constraints. The formulation involves defining decision variables, an objective function, and constraints, and then solving the model to identify the most profitable purchase combination. Formulation of the Linear Programming Model Let: X₁ = gallons of Yodel to stock X₂ = gallons of Shotz to stock X₃ = gallons of Rainwater to stock The objective is to maximize net profit, which is the difference between selling revenue and purchase cost: Maximize Z = (3.00 - 1.50) X₁ + (2.50 - 0.90) X₂ + (1.75 - 0.50) * X₃ which simplifies to: Maximize Z = 1.50 X₁ + 1.60 X₂ + 1.25 * X₃ Subject to the following constraints: Budget Constraint: 1.50 X₁ + 0.90 X₂ + 0.50 * X₃ ≤ 2000 Total Capacity: X₁ + X₂ + X₃ ≤ 1000 Demand Constraints: X₁ ≤ 400 X₂ ≤ 500 X₃ ≤ 300 Non-negativity: X₁, X₂, X₃ ≥ 0 This model ensures that Betty stocks the optimal combination of beers to maximize her profit while respecting capacity, budget, and demand limits. Solution Approach The linear programming model can be solved using computer-based methods such as the Simplex algorithm. Software tools like LINDO, Excel Solver, or specialized LP solvers can handle such models efficiently. The solution will provide the quantities of each beer brand Betty should order to achieve maximum profit. Implications and Recommendations Applying this model allows Betty to make data-driven stocking decisions that maximize her profit margin. It ensures her inventory is constrained within budget and capacity while meeting customer demand. This approach minimizes the risk of overstocking or understocking, which could either lead to lost sales or excess inventory costs. Additionally, sensitivity analysis can be perfo

Betty Malloy, Owner Of The Eagle Tavern In Pittsburgh

Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing

Paper For Above instruction

Formulation of the Linear Programming Model

Solution Approach

Implications and Recommendations

References