Sanotronics $LLCis$ a start$-up$ company that manufactures medical devices for use $in$ hospital clinics. Inspired $by$ experiences with family members who have battled cancer, Sanotronics$s$ founders have developed a prototype for a new device that $limits$ health care workers$$ exposure $to$ chemotherapy treatments while they are preparing, administering, and disposing $of$ these hazardous medications. The new device features $an$ innovative design and has the potential $to$ capture a substantial share $of$ the market.

Sanotronics would like $an$ analysis $of$ the first$-$year profit potential for the device. Because $of$ Sanotronics$s$ tight cash flow situation, management $is$ particularly concerned about the potential for a loss. Sanotronics has identified the key parameters $in$ determining first$-$year profit: selling price per unit $(p),$ first$-$year administrative and advertising costs $(Ca),$ direct labor cost per unit $(CL),$ parts cost per unit $(Cp),$ and first$-$year demand $(d).$ After conducting market research and a financial analysis, Sanotronics estimates with a high level $of$ certainty that the device$s$ selling price will $be$ $$249$ per unit and that the first$-$year administrative and advertising costs will total $$1,000,000.$

Sanotronics $is$ not certain about the values for the cost $of$ direct labor, the cost $of$ parts, and the first$-$year demand. $At$ this stage $of$ the planning process, Sanotronics$s$ base estimates $of$ these inputs are $$45$ per unit for the direct labor cost, $$90$ per unit for the parts cost, and $15,000$ units for the first$-$year demand.

Based $on$ recent wage rates and estimated processing requirements $of$ the device, Sanotronics believes that the direct labor cost will range from $$43to$ $$47$ per unit and $is$ described $by$ the discrete probability distribution. There $isa10\%$ probability that the direct labor cost will $be$ $$43$ per unit, $a20\%$ probability that the direct labor cost will $be$ $$44$ per unit, $40\%it$ will $be$ $$45,20\%it$ will $be$ $$46,$ and $10\%$ that $it$ will $be$ $$47.$

Sanotronics $is$ relatively unsure $of$ the parts cost because $it$ depends $on$ many factors, including the general economy, the overall demand for parts, and the pricing policy $of$ Sanotronics$s$ parts suppliers. Sanotronics $is$ confident that the parts cost will $be$ between $$80$ and $$100$ per unit but $is$ unsure $asto$ whether any particular values between $$80$ and $$100$ are more likely than others. Therefore, Sanotronics decides $to$ describe the uncertainty $in$ parts cost with a uniform probability distribution.

Based $on$ sales $of$ comparable medical devices, Sanotronics believes that first$-$year demand $is$ described $by$ the normal probability distribution. The mean $of$ first$-$year demand $is15,000$ units and the standard deviation $of4,500$ units describes the variability $in$ the first$-$year demand.