53. The annual demand for Prizdol, a prescription drugmanufactured and marketed by the NuFeel Company,is normally distributed with mean 50,000 and standarddeviation 12,000. Assume that demand during each ofthe next 10 years is an independent random numberfrom this distribution. NuFeel needs to determine howlarge a Prizdol plant to build to maximize its expectedprofit over the next 10 years. If the company builds aplant that can produce x units of Prizdol per year, it willcost $16 for each of these x units. NuFeel will produceonly the amount demanded each year, and each unit ofPrizdol produced will sell for $3.70. Each unit of Prizdol produced incurs a variable production cost of $0.20.It costs $0.40 per year to operate a unit of capacity.a. Among the capacity levels of 30,000, 35,000,40,000, 45,000, 50,000, 55,000, and 60,000 unitsper year, which level maximizes expected profit?Use simulation to answer this question.b. Using the capacity from your answer to part a,NuFeel can be 95% certain that actual profit for the10-year period will be between what two values?
53. The annual
manufactured and marketed by the NuFeel Company,
is
deviation 12,000. Assume that demand during each of
the next 10 years is an independent random number
from this distribution. NuFeel needs to determine how
large a Prizdol plant to build to maximize its expected
profit over the next 10 years. If the company builds a
plant that can produce x units of Prizdol per year, it will
cost $16 for each of these x units. NuFeel will produce
only the amount demanded each year, and each unit of
Prizdol produced will sell for $3.70. Each unit of Prizdol produced incurs a variable production cost of $0.20.
It costs $0.40 per year to operate a unit of capacity.
a. Among the capacity levels of 30,000, 35,000,
40,000, 45,000, 50,000, 55,000, and 60,000 units
per year, which level maximizes expected profit?
Use simulation to answer this question.
b. Using the capacity from your answer to part a,
NuFeel can be 95% certain that actual profit for the
10-year period will be between what two values?
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