Philip P. answered • 11/03/17

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Effective and Patient Math Tutor

R(x) = (number of units rented)(price per unit)

R(x) = (800 + 20x)(300 - 5x)

where x = the number of $5 decreases in rent. x must be less than or equal to 40 because you only have 1600 units total. Multiplying out the two binomials in R(x) gives:

**R(x) = -100x**

^{2}+ 2000x + 240,000R(x) is an inverted parabola, so the vertex will be the maximum revenue. Complete the square on R(x) to put it into the vertex form y = a(x-h)

^{2}+k where (h, k) is the location of the vertex.:R(x) = -100(x

^{2}- 20x + (-10)^{2}) + 240,000 + (100)(10^{2})R(x) = -100(x-10)

^{2}+ 250,000The vertex is located at (10, 250,000). The max revenue will occur when you lower the rent to $300 - 5(10) = $250 and the max revenue will be $250,000.