Maximizing Profit with Resource Constraints?

📌 CONCEPT: A linear programming problem is formulated to maximize profit by determining the optimal production levels of smartphones and laptops, subject to resource constraints on labour and memory.

📐 RULE / FORMULA: The objective function represents the profit to be maximized, while the constraints represent the labour and memory availability. The constraints can be represented as inequalities, where the resources are allocated to the production of smartphones and laptops.

💡 WORKED EXAMPLE: Consider a company that can produce either smartphones or laptops, with a profit of ₹800 from each smartphone and ₹1200 from each laptop. The company has 800 hours of labour and 400 units of memory available. To maximize profit, we can formulate the linear programming problem as:

Maximize P = 800x + 1200y

Subject to:

8x + 6y ≤ 800 (labour constraint)

4x + 3y ≤ 400 (memory constraint)

x ≥ 0 (non-negativity constraint)

y ≥ 0 (non-negativity constraint)

⚠️ COMMON MISTAKE: Students often forget to include the non-negativity constraints, which can lead to incorrect solutions.