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Social ScienceaLumyn Electronics is currently renting their store space from Quality Holdings Corp.Quality Holdings owns a total of 250 commercial properties available for rent. The company's monthly profit, P, in dollars, is given by the equationP(n) = -8n2 + 3,200n – 80,000where n is the number of properties rented during a particular month.a) Would renting out all of the available properties maximize Quality Holdings’ profit?b) If not, what is the optimum number of properties that the company must have rented in order to maximize its profit?
a
Lumyn Electronics is currently renting their store space from Quality Holdings Corp.
Quality Holdings owns a total of 250 commercial properties available for rent. The company's monthly profit, P, in dollars, is given by the equation
P(n) = -8n2 + 3,200n – 80,000
where n is the number of properties rented during a particular month.
a) Would renting out all of the available properties maximize Quality Holdings’ profit?
b) If not, what is the optimum number of properties that the company must have rented in order to maximize its profit?
Expert Answer
The company's monthly profit, P, in dollars, is given by the equation
P(n) = -8n2 + 3,200n – 80,000
where n is the number of properties rented during a particular month.
For a maximum or minimum, dP(n) / dn = 0.
Hence, -16n + 3,200 = 0
Hence, n* = 3,200 / 16 = 200
Check the sign of dP2(n) /dn2 at n = n* = 200
dP2(n) /dn2 = -16 which is negative irresepctive...
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Calculus
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