. Collect relevant data to apply a linear optimization model to solve the problem. The business can be one of the following: grocery, bakery, supermarket, restaurant, hotel, bank, airline, toys, or any production/manufacturing. You will demonstrate in the model either one of the following: to maximize profit, productivity, efficiency, and customer satisfaction or to minimize cost or defect. Conduct the following linear optimization steps:
1. Present the data and mathematical linear optimization model.
2. Identify and define decision variables.
3. Formulate the objective function.
4. Identify the set of constraints.
5. Solve the linear optimization model using the Solver.
6. Summarize Solver results in a written memo report addressed to the company management. Provide a brief action plan for the implementation of the model.
The general form of the linear optimization model is:
Maximize Z=c1x1+c2x2+…Subject to: ai1x1+ai2x2+⋯≤bixj≥0(Non-negativity)
For The Daily Loaf:
Maximize Z=8L+5CSubject to:Labor Constraint: 10L+15C≤1200Oven Time Constraint: 35L+15C≤1050Min Demand - Loaf: L≥20Min Demand - Croissant: C≥15Non-negativity: L≥0,C≥0 (Implied by Min Demand)
2. Identify and Define Decision Variables
The decision variables represent the quantities that the management can control and that directly impact the objective function.
L: The number of Sourdough Loaves to produce daily.
C: The number of Signature Croissants to produce daily.
3. Formulate the Objective Function
The objective is to maximize the total daily profit (Z).
Profit per Loaf is $8.00.
Profit per Croissant is $5.00.
Maximize Z=8L+5C
4. Identify the Set of Constraints
The constraints are the limitations imposed by resources and minimum sales targets.
Labor Constraint (Time in minutes): The time spent preparing and finishing the products cannot exceed the total available labor time (1,200 minutes).
- 10L+15C≤1200
Oven Time Constraint (Time in minutes): The time the products spend occupying the oven cannot exceed the total available oven time (1,050 minutes).
- 35L+15C≤1050
Minimum Demand Constraints: The bakery must meet its expected minimum daily sales for quality of service.