$1.[10$ pts$]$ Cost Estimating: Dell has $6$ days of inventory, Gateway has $3$ weeks. Inventory cost is $0\mathrm{.}8\%/$ week of inventory. Dell$$s net profit is $4\mathrm{.}5\%.$ Assume all else is equal and estimate Gateway$$s profit.

$2.[20$ pts$]$ Optimization: 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, 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.

Department Monthly Hours

Available Hours $/$ Unit

$($Electronic$)$ Hours $/$ Unit

$($Battery$)$

Fabrication $24000\mathrm{.}150\mathrm{.}10$

Assembly $42000\mathrm{.}200\mathrm{.}20$

Shipping $20000\mathrm{.}100\mathrm{.}15$

Variable cost $/$ unit $$17\mathrm{.}00$ $$16\mathrm{.}00$

Retail Price $$30\mathrm{.}00$ $$28\mathrm{.}00$

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 $$20\mathrm{.}00$ per unit. For this price, the subcontractor will test and ship its models directly to the retailers without using Acme$$s production process

Determine how the manufacturer should allocate its in$-$house capacity and how it should utilize the subcontractor. What are the maximum profit and corresponding make$/$buy levels?