2.8 Make or Buy: A sudden increase in the demand for smoke detectors has left Acme Alarms with insufficient capacity to meet demand. The company has seen monthly demand for its electronic and battery-operated detectors rise to 20,000 and 10,000, respectively, and Acme wishes to continue meeting demand. Acme's production process involves three departments: fabrication, assembly, and shipping. The relevant quantitative data on production and prices are summarized below. Monthly Hours Hours/Unit Hours/Unit Department Available (Electronic) (Battery) Fabrication 2000 0.15 0.10 Assembly 4200 0.20 0.20 Shipping 2500 0.10 0.15 Variable cost/unit $18.80 $16.00 Retail price $29.50 $28.00 The company also has the option to obtain additional units from a subcon- tractor, who has offered to supply up to 20,000 units per month in any combination of electronic and battery-operated models, at a charge of $21.50 per unit. For this price, the subcontractor will test and ship its models directly to the retailers without using Acme's production process. (a) What are the maximum profit and the corresponding make/buy levels? (This is a planning model, and fractional decisions are acceptable.) (b) Trace the effects of increasing fabrication capacity by 10%. How will the optimal make/buy mix change? How will the optimal profit change?

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