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Elliott Gorsuch

Optimization Model for a Small Bakery

Problem Statement:

Developing an optimization model to maximize the profit for a small bakery. The model includes various constraints such as ingredient availability, production capacity, and demand.

Goals:

Learn to build a robust optimization model that can determine the optimal production quantities for various bakery items to achieve maximum profit.

  • Data Collection: Data was given on ingredient availability, production capacity, demand for bakery items, and profit margins.

  • Optimization Techniques: The model uses linear programming to determine the optimal production quantities. The PuLP library in Python is used to formulate and solve the optimization problem.

Methodology

Results

  • The optimization model minimized the cost of producing 350 low-fat cookies and 500 regular cookies, achieving a total cost of $140.96.

  • The model determined that for low-fat cookies, the optimal ingredient weights are 7.0 lbs of peanut butter, 6.125 lbs of eggs, and 4.375 lbs of sugar.

  • For regular cookies, the optimal ingredient weights are 16.0 lbs of peanut butter, 2.75 lbs of eggs, and 6.25 lbs of sugar.

  • These results ensure that all constraints regarding ingredient availability and usage percentages are satisfied while minimizing production costs.

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