To guarantee that the correct answer yields an integer value for the number of days, the prompt should include the following condition in blue:
fozzzy wrote:
A manufacturer can save x dollars per unit in production costs by overproducing in certain seasons. Storage costs for the excess are y dollars per unit per day, where x/y is an integer. Which of the following expresses the maximum number of days that n excess units can be stored before the storage costs exceed the savings on the excess units?
A) \(x - y\)
B) \((x - y)n\)
C) \(\frac{x}{y}\)
D) \(\frac{xn}{y}\)
E) \(\frac{x}{yn}\)
Let n=2 excess units.
Let x=$100 production savings per unit, implying that the total production savings for 2 units = 2*100 = $200.
Let y=$10 daily storage cost per unit, implying that the daily storage cost for 2 units = 2*10 = $20.
Which of the following expresses the maximum number of days that n excess units can be stored before the storage costs exceed the savings on the excess units?Since the storage costs may not exceed the $200 in production savings, the maximum total storage cost = $200.
At a rate of $20 per day, the greatest number of storage days that can be purchased for $200 \(= \frac{200}{20} = 10\).
The correct answer must yield 10 when x=100, y=10 and n=2.
Only C works:
\(\frac{x}{y} = \frac{100}{10} = 10\)
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