1. **State the problem:** Minimize the total manufacturing cost for Bataan Electronics Manufacturing Inc. by determining the optimal monthly production quantities of LED Light Assemblies ($x$) and Circuit Board Modules ($y$) subject to machine, labor, quality control, and market constraints. 2. **Define variables:** Let $x$ = number of LED Light Assemblies produced per month. Let $y$ = number of Circuit Board Modules produced per month. 3. **Calculate unit variable costs:** LED Light Assembly variable cost = direct materials + direct labor + variable overhead = $125 + 80 + 45 = 250$ Circuit Board Module variable cost = $180 + 110 + 60 = 350$ 4. **Formulate the objective function (minimize total manufacturing cost):** Total variable cost = $250x + 350y$ Total fixed cost = $285,000 + 195,000 + 220,000 = 700,000$ Objective function: $$\text{Minimize } Z = 250x + 350y + 700000$$ 5. **Write constraints:** - SMT machine hours limit: $$1.5x + 3y \leq 4500$$ - Assembly line hours limit: $$0.8x + 1y \leq 2000$$ - Quality control testing equipment ratio (at least 2 LED assemblies per 1 circuit board): $$2x \geq y$$ - Export order commitments (minimum production): $$x \geq 1000$$ $$y \geq 400$$ - BOI tax incentive minimum production: $$x + y \geq 1599$$ - Non-negativity: $$x \geq 0, \quad y \geq 0$$ 6. **Summary of the linear programming model:** $$\begin{cases} \text{Minimize } Z = 250x + 350y + 700000 \\ 1.5x + 3y \leq 4500 \\ 0.8x + y \leq 2000 \\ 2x \geq y \\ x \geq 1000 \\ y \geq 400 \\ x + y \geq 1599 \\ x, y \geq 0 \end{cases}$$ 7. **Should the company avail of the BOI incentive?** Yes, because producing at least 1599 units monthly qualifies the company for a 60% tax subsidy on corporate tax, significantly reducing tax expenses and improving profitability. **Final answer:** The linear programming model above determines the optimal production quantities $x$ and $y$ to minimize total manufacturing cost while satisfying all constraints. Availing the BOI incentive is beneficial due to the substantial tax subsidy.