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The manager of a 100-unit apartment complex knows from experience that all units will be occupied if the rent is $500 per month. A market survey suggests that, on average, one additional unit will remain vacant for each $10 increase in rent. What rent should the manager charge to maximize revenue?

Respuesta :

Paounn

Answer:

750$

Step-by-step explanation:

lets say the increase is x times 10$. it means manager asks for (500+10x) and earns it from (100-x) apartments. Revenue will be the product of the two:

[tex](500 + 10x)(100 - x) = 50 \: 000 - 500x + 1 \: 000x - 10 {x}^{2} = 50000 + 500x - 10 {x}^{2} [/tex]

its a parabola, and its maximum is on the vertex, or at

[tex]x = - \frac{b}{2a} = - \frac{500}{ - 20} = 25[/tex]

so he should add 10$ 25 times, or ask 750$