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Next Page Page 5 of 6 Note: t is recommended that you save your response as you complete each question Question 5 (1 point) Many treatment facilities overbook customer demand to assure there is no shortage of capacity Some customers have regular water and wastewater demand that is consistently scheduled in advance, while other customer demand may run from or to their treatment facility around other events that can influence demand (i.e. community event, holiday, etc.) The treatment facility estimates that their employee s capacity is 7,500 gallons per day (per 8 hour shit). Each employee costs $2 25 per gallon. If customer demand exceeds capacity, the treatment facility has to arrange for employees on-call to come in and operate a back-up system support the overload. This requires an added fee which results in a loss of $7.50 per gallon. Customer demand may not be regular or consistent. These issues are normally distributed with a mean of 350 gallons and a standard deiation of 100 gallons. What should the treatment facility decide regarding how many gallons it will overbook the facility? 163 o 54 29 276 Save Page 5 of b Next Page Save All Responses Go to Submit Quiz

Explanation / Answer

Here overage cost = c -s = $ 2.25 per gallon

underage cost = p - c = $ 7.5 per gallon

so Pr(do not sell Q + 1 unit) = F(Q) = 2.25 / (2.25 + 7.5) = 0.23

so Here the mean = 350 gallons

Standard deviation = 100 gallons

Pr(x < X ; 350 ; 100) = 0.23

Z value for the given p - value = -0.739

so Z = (X - 350)/100 = -0.739

X = 350 - 100 * 0.74 = 276

Option D is correct.

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