Make or Buy Decision for Acme Alarms: A Comprehensive Analysis

  Make or Buy Decision for Acme Alarms: A Comprehensive Analysis Thesis Statement In the face of unprecedented demand for smoke detectors, Acme Alarms must strategically evaluate whether to increase internal production capacity or outsource production to a subcontractor. This analysis will determine the most profitable approach for meeting demand while considering production constraints and costs. Introduction Acme Alarms is currently experiencing a surge in demand for its electronic and battery-operated smoke detectors. With the monthly demand reaching 20,000 units for electronic detectors and 10,000 units for battery-operated ones, the company faces a critical decision: Should it expand its production capacity or outsource to a subcontractor? This essay will analyze both options to identify the maximum profit levels and corresponding make/buy decisions. Part A: Maximum Profit and Corresponding Make/Buy Levels 1. Calculate Production Capacity To assess the feasibility of meeting demand internally, we need to analyze the availability of hours in each department against the time required per unit. - Fabrication: - Monthly Hours Available: 2,000 - Hours/Unit (Electronic): 0.15 - Hours/Unit (Battery): 0.10 [ \text{Max Units Fabrication} = \frac{2,000}{0.15} = 13,333 \text{ (Electronic)} ] [ \text{Max Units Fabrication} = \frac{2,000}{0.10} = 20,000 \text{ (Battery)} ] - Assembly: - Monthly Hours Available: 4,200 - Hours/Unit (Electronic): 0.20 - Hours/Unit (Battery): 0.20 [ \text{Max Units Assembly} = \frac{4,200}{0.20} = 21,000 \text{ (Both)} ] - Shipping: - Monthly Hours Available: 2,500 - Hours/Unit (Electronic): 0.10 - Hours/Unit (Battery): 0.15 [ \text{Max Units Shipping} = \frac{2,500}{0.10} = 25,000 \text{ (Electronic)} ] [ \text{Max Units Shipping} = \frac{2,500}{0.15} = 16,667 \text{ (Battery)} ] 2. Identify Constraints Given the monthly demand of 20,000 electronic and 10,000 battery-operated detectors, we face constraints in Fabrication and Shipping departments: - Fabrication can produce a maximum of 13,333 electronic and 20,000 battery-operated units. - Shipping can handle up to 25,000 electronic and 16,667 battery-operated units. 3. Optimal Production Mix Calculation [ \text{Profit from Electronic} = (\text{Price} - \text{Variable Cost}) * \text{Units Produced} ] [ \text{Profit from Battery} = (\text{Price} - \text{Variable Cost}) * \text{Units Produced} ] - Profit Calculations: For Electronic: - Profit per unit: $29.50 - $18.80 = $10.70 - Maximum profit if all electronic produced: [ 10.70 * 13,333 = $142,074 ] For Battery: - Profit per unit: $28.00 - $16.00 = $12.00 - Maximum profit if all battery produced: [ 12.00 * 10,000 = $120,000 ] Total Profit from Internal Production Using maximum limits: - Electronic: Production = 13,333 - Battery: Production = 10,000 Total Profit: [ $142,074 + $120,000 = $262,074 ] Outsourcing Decision Outsourcing cost per unit from subcontractor is $21.50. To find profits when buying: - If Acme buys units from subcontractor: [ Profit from Outsourced Electronic = (29.50 - 21.50) * x ] [ Profit from Outsourced Battery = (28.00 - 21.50) * y ] Setting total units to demand yields: [ Profit = (8 * x) + (6.50 * y) ] Cost-effectiveness indicates that producing in-house is better unless exceeding capacity where outsourcing becomes necessary. Part B: Integer Decision Optimization The requirement for integer solutions necessitates calculating how many units to produce versus buy without fractional units. Production Constraints with Integer Decisions: - Fabrication limits production closer to maximum capabilities. - Rounding decisions may lead to loss of profit. Assuming maximum capacity without exceeding limits leads to: - Produce all feasible electronic units: 13,333 - Produce all battery-operated units: 10,000 If production runs are rounded down or adjusted for integer solutions: 1. Adjust for integer so that production remains feasible without exceeding limits. By adjusting unit products according to capacities and trade-offs between production and outsourcing offers a comprehensive profit scenario. Part C: Analysis of Integer Solutions Compared to Fractional Solutions The integer solution may not always align directly with the fractional solution established earlier due to practical constraints in production lines or resource availabilities. It's vital to evaluate whether rounding off affects overall profitability and operational efficiency. Often in integer solutions: - Reductions in production lead to less than optimal profit margins. - The integer solution may lead to a profit reduction due to constraints in producing fractional units. Conclusion In conclusion, Acme Alarms faces a critical decision regarding the production of smoke detectors amidst rising demand. By conducting a detailed analysis of both internal production and outsourcing options, Acme can determine the most profitable strategy. The findings suggest that while internal production is optimal under certain capacities, the ability to adjust for integer solutions must be considered to ensure operational feasibility and maximum profit retention. Ultimately, a balanced approach that weighs production capabilities against outsourcing potential will provide Acme Alarms with the best route forward in navigating increased market demand effectively.      

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