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 from its

retailers for its electronic and battery$-$operated detectors rise to $20,000$ and $10,000,$ respectively. Acme's production process involves three departments: fabrication, assembly, and

shipping. The relevant quantitative data on production and prices are summarized as follows:

The company also has the option to obtain additional units from a subcontractor, who has offered to supply up to $20,000$ units per month in any combination of electric and battery$-$

operated models, at a charge of $$21\mathrm{.}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? $($Fractional decisions are acceptable.$)$

b$.$ Describe the qualitative pattern in the solution.

c$.$ Use the pattern in $(b)$ to trace the effects of increasing the fabrication capacity by $10$ percent. How will the optimal make$/$buy mix change? How will the optimal profit change?

d$.$ For how much of a change in fabrication capacity will the pattern persist?