1. **State the problem:** We want to maximize the total profit from producing two components, C1 and C2, given constraints on costs, production capacity, and available resources. 2. **Define variables:** Let $x$ = number of units of C1 produced Let $y$ = number of units of C2 produced 3. **Calculate profit per unit:** - Cost per unit of C1 = wages + material = $5 + 5 = 10$ - Selling price of C1 = $30$ - Profit per unit of C1 = $30 - 10 = 20$ - Cost per unit of C2 = wages + material = $25 + 15 = 40$ - Selling price of C2 = $70$ - Profit per unit of C2 = $70 - 40 = 30$ 4. **Objective function:** Maximize total profit: $$\text{Maximize } Z = 20x + 30y$$ 5. **Constraints:** - Initial cash balance to pay wages and materials: $10x + 40y \leq 4000$ - Machine time: $3x + 2y \leq 2000$ - Assembly time: $2x + 3y \leq 1400$ - Non-negativity: $x \geq 0, y \geq 0$ 6. **Summary:** The LP model is: $$\max Z = 20x + 30y$$ subject to $$10x + 40y \leq 4000$$ $$3x + 2y \leq 2000$$ $$2x + 3y \leq 1400$$ $$x, y \geq 0$$ This model maximizes profit while respecting cash, machine, and assembly time constraints.