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 ship$-$

ping. 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 months 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 proccess.

#$1$ What are the maximum profits available to Acme Alarms if you allow fractional decisions? $$298,000$

#$2$ How many electronic smoke alarms should Acme Alarms make $($assuming fractional decisions are allowed$)?$

#$3$ How many electronic alarms should Acme Alarms buy $($now all decisions should be constrained to be integers$)?$