The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 392 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 7 dollar increase in rent. Simarly, one additional unit will be occupied for each 7 dollar decrease in rent. (a) If x is the number of units rented, and p is the rent per unit in dollars, what is the price-demand equation (assuming it is linear)? p=_____ (b) What is the monthly revenue function? R(x)=____ (c) How many apartment units should be rented to maximize the monthly revenue? ____ apartment units (d) What is th monthly revenue for the manager? Round your answer to the nearest cent if necessary. ___ dollars (e) What rent should the manager charge to maximize the monthly revenue? Round your answer to the nearest cent if necessary. ___ dollars per un
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 392 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 7 dollar increase in rent. Simarly, one additional unit will be occupied for each 7 dollar decrease in rent.
(a) If x is the number of units rented, and p is the rent per unit in dollars, what is the price-demand equation (assuming it is linear)?
p=_____
(b) What is the monthly revenue function?
R(x)=____
(c) How many apartment units should be rented to maximize the monthly revenue?
____ apartment units
(d) What is th monthly revenue for the manager? Round your answer to the nearest cent if necessary.
___ dollars
(e) What rent should the manager charge to maximize the monthly revenue? Round your answer to the nearest cent if necessary.
___ dollars per unit
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