5A company produces two products, A and B, using machine hours and labor hours. Each unit of Product A requires 3 machine hours and 2 labor hours, while each unit of Product B requires 2 machine hours and 4 labor hours. The company has 180 machine hours and 240 labor hours available per day. If the profit per unit is $10 for Product A and $15 for Product B, how many units of Product B should be produced to maximize profit? - Coaching Toolbox
5A Company’s Product Mix: How to Maximize Profit from Machine and Labor Hours
5A Company’s Product Mix: How to Maximize Profit from Machine and Labor Hours
With rising focus on efficient manufacturing and smart resource allocation, many businesses are evaluating how to balance production across products to boost profit. 5A Company exemplifies this challenge by managing two distinct products—A and B—within strict daily limits of machine and labor hours. This scenario reflects a growing trend among U.S. manufacturers aiming to optimize output without overextending capacity.
The core of 5A’s production puzzle lies in two clear constraints: 180 machine hours and 240 labor hours each day. Each unit of Product A demands 3 machine hours and 2 labor hours, while Product B uses 2 machine hours and 4 labor hours. With a $10 profit per unit for A and $15 for B, the real question becomes: which mix delivers the highest profit?
Understanding the Context
Why this Matters in Today’s Market
Manufacturing efficiency is no longer optional—it’s essential for competitiveness. As supply chain dynamics shift and labor costs remain tight, companies are increasingly analyzing how to balance labor and machine usage across product lines. For US-based manufacturers, understanding these resource constraints helps align operations with real-world limitations while pursuing profit growth. This type of problem isn’t just theoretical—it’s reshaping daily decisions for operations teams across industries.
How 5A Company Balances Production Lines
5A’s profit model centers on two inputs: machine hours and labor hours. With 180 machine hours available and 240 labor hours, the challenge is how to allocate each product’s support. Each unit of A consumes 3 machine hours and 2 labor hours; each unit of B uses 2 machine hours and 4 labor hours. Profit margins of $10 for A and $15 for B mean every unit produced contributes differently to the bottom line.
The optimal production mix depends on maximizing total profit per hour of constrained resources. By analyzing constraint boundaries, 5A can determine the units of B that best leverage both inputs. This approach favors products with higher profit per available hour, adjusting based on actual hour usage.
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Key Insights
Key Considerations for Production Decisions
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Resource Trade-offs: Product A uses more labor per hour but less machine time, while B offers more machine usage per unit but higher labor demand.
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Profit Efficiency: Despite lower machine use, B’s higher profit per unit makes it a strong candidate when labor hours allow.
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Capacity Limits: Without exceeding daily constraints, production planes must stay within 180 machine and 240 labor hours.
Maximizing Product B units increases profit to a peak, but only when both inputs remain within limits—balancing output with operational reality.
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Common Questions About Product B’s Production Role
H3: Does focusing on Product B always drive higher profit?
While Product B offers greater profit per unit, increasing its output may strain machine hours if labor hours are limited. Profit maximization requires evaluating both products’ hour usage relative to daily availability—sometimes higher B production slows progress on A, offsetting gains.
H3: How do machine and labor hours affect total profit?
Each hour applied to A yields $10/3 ≈ $3.33 per machine hour, while B generates $15/2 = $7.50 per labor hour. The trade-off highlights B’s ability to generate faster profit per labor hour, making it strategically valuable when labor constraints permit.
Opportunities and Catch-Strategies
Maximizing Product
