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CalculusQ&A LibraryaLumyn 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?Question

Asked Feb 8, 2019

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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?

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Step 1

The company's monthly profit, P, in dollars, is given by the equation

P(n) = -8n^{2} + 3,200n – 80,000

where n is the number of properties rented during a particular month.

Step 2

For a maximum or minimum, dP(n) / dn = 0.

Hence, -16n + 3,200 = 0

Hence, n* = 3,200 / 16 = 200

Step 3

Check the sign of dP2(n) /dn2 at n = n* = 200

dP2(n) /dn2 = -16 which is negative irresepctive...

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