3223-10 - Free Printable

- The objective is to maximize profit: max x₁ + 6x₂.
- Constraints are:
- x₁ ≤ 200 (demand limit for Pyramide)
- x₂ ≤ 300 (demand limit for Nuit)
- x₁ + x₂ ≤ 400 (total production capacity)
- x₁, x₂ ≥ 0 (non-negativity)
- Since the profit per unit of Nuit ($6) is much higher than Pyramide ($1), we prioritize producing as much Nuit as possible.
- The maximum allowed Nuit is min(300, 400) = 300 (due to demand and total capacity).
- If x₂ = 300, then from x₁ + x₂ ≤ 400, we get x₁ ≤ 100.
- Also, x₁ ≤ 200 is satisfied since 100 < 200.
- So, set x₁ = 100, x₂ = 300.
- Profit = 100×1 + 300×6 = 100 + 1800 = 1900.
- This point (100, 300) satisfies all constraints and gives maximum profit.
- Any other combination would either violate a constraint or yield lower profit.

Optimal solution: x₁ = 100, x₂ = 300.