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Study Case: Optimization Model
Ming Zhao
College of Business, Westcliff University
DATA 800 Foundations in Analytics for Executives
Professor Manase
April 14, 2024
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Study Case: Optimization Model
This assignment aims to create an optimization model for an optimal production
schedule. Suppose a company produces two products, Product A and Product B. The goal is to
determine the optimal production quantities for each product to meet the demand while
minimizing production costs. The decision variables are x1, representing the quantity of Product
A to produce, and x2, denoting the quantity of Product B to produce. The objective function is
Z=50x1+80x2. Specifically, the objective is to minimize the total production cost Z, which is the
sum of the costs associated with producing Product A and Product B. The constraints include
two demand constraints and one production capacity constraint. The demand constraints are that
x1  100 and x2  150. The capacity constraint is x1+x2  300.
I use SciPy from Python to solve this optimization problem. To summarize, we need to
minimize Z = 50x1+80x2 subject to x1  100, x2  150, and x1+x2  300. After setting up the
optimization model in Python, the optimal solution for the production schedule is x1=100 and
x2=150. Therefore, the total cost production Z=50100+80150=17000. That is, the optimal total
cost is $17000 when producing 100 unite of Product A and 150 units of Product B. This solution
satisfies the demand constraints for both products and the production capacity constraints.
Alternatively, we can also use graphical method to solve this optimization problem. The
plot below shows the optimal solution. The three blues lines represent the three constraints. The
blue triangle is the feasible region and its points are feasible solutions. Since we want to
minimize Z, point (100, 150) is the best solution.
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