Business example of linear programming.

 

Research in the library, the textbook, and/or online to find a business example of linear programming.
You may use any business-related example you desire as long as it contains the information you need to show your knowledge of linear programming to complete the paper successfully.
In your paper,

Describe how and why your chosen business example deployed linear programming.
Analyze the method of linear programming used by your chosen company. Did it work in their favor? Would you recommend a different methodology?
Explain how the business used linear programming to optimize resources like budget, time, people, and/or machinery.
List the benefits that this business received as a result of deploying linear programming.

 

Sample Answer

 

 

 

 

 

 

 

🏭 Business Example of Linear Programming: Resource Allocation in Manufacturing

 

A common and highly effective business application of linear programming (LP) is in resource allocation and production planning within the manufacturing sector. I'll use a hypothetical, but representative, example of a large electronics manufacturer, TechCorp, that produces two primary products: Smartwatches (S) and Fitness Trackers (F).

 

Deployment of Linear Programming

 

TechCorp deployed linear programming to solve a classic optimization problem: How many Smartwatches (S) and Fitness Trackers (F) should they produce daily to maximize profit, given limited resources?

Why Linear Programming?

TechCorp used LP because their problem met the key criteria:

Clear Objective: Maximize total profit.

Constraints: Production is limited by tangible, quantifiable resources (machine hours, labor hours, components).

Linear Relationships: The relationship between production quantity and both profit and resource consumption is linear.

The LP Model Structure:

ElementDescription
Decision Variables$S$ = Number of Smartwatches produced per day; $F$ = Number of Fitness Trackers produced per day.
Objective FunctionMaximize $Z$ (Profit): Maximize $Z = 50S + 30F$ (Assuming profit is $\$50$ per Smartwatch and $\$30$ per Tracker).
ConstraintsMachine Time: $2S + 1F \le 400$ (Machine hours available per day).
 Labor Hours: $1S + 1F \le 300$ (Labor hours available per day).
 Non-Negativity: $S \ge 0$, $F \ge 0$.

 

Analysis of the Linear Programming Method

 

TechCorp primarily used the Simplex Method to solve this LP problem, which is the standard, reliable algorithm for analyzing multi-variable linear inequalities.

Did it Work in Their Favor?

Yes, the method worked effectively. The Simplex Method determined the optimal production plan to be the following:

Produce 100 Smartwatches ($S=100$).

Produce 200 Fitness Trackers ($F=200$).

Maximum Daily Profit ($Z$) = $\$50(100) + \$30(200) = \$5,000 + \$6,000 = \$\mathbf{11,000}$.

This result ensured that they utilized all available labor hours and all but 100 machine hours, achieving the highest possible profit under current constraints.

Recommendation for a Different Methodology: