$1.[10pts]$ Cost Estimating: Dell has $6$ days $of$ inventory, Gateway has $3$ weeks. Inventory cost $is0\mathrm{.}8\%\frac{?}{?}$ week $of$ inventory. Dell$s$ net profit $is4\mathrm{.}5\%.$ Assume all else $is$ equal and estimate Gateway$s$ profit.

$2.[20pts]$ 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 $to20,000$ 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 $upto20,000$ 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 mak$\frac{e}{b}uy$ levels?