The manager of a large apartment complex knows from experience that 85 units will be occupied if the rent is $ 800 per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 5 dollar increase in rent. Similarly, one additional unit will be occupied for each 5 dollar decrease in rent. (A) If the rent is $ 800 and indeed 85 units are filled, how much does the apartment manager make in that month? (B) The manager is trying to find the right monthly charge to get the best net revenue. ... Mathematics to the rescue! Let x be the rent for one unit in a given month. We'll write a function that describes his expected revenue as a function of x. First write a function for the number of units filled as a function of x. Hint: you know several points on this function and you know what type of function it is. Units(x) = Now write a function for the revenue that the apartment manager makes as a function of x. Revenue(x) = Finally, Plot the revenue function and verify visually that there is a rent that can be charged that gives a maximum revenue.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
The manager of a large apartment complex knows from experience that 85 units will be occupied if the rent is $ 800 per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 5 dollar increase in rent. Similarly, one additional unit will be occupied for each 5 dollar decrease in rent.
(A) If the rent is $ 800 and indeed 85 units are filled, how much does the apartment manager make in that month?
(B) The manager is trying to find the right monthly charge to get the best net revenue. ... Mathematics to the rescue! Let x be the rent for one unit in a given month. We'll write a function that describes his expected revenue as a function of x.
First write a function for the number of units filled as a function of x. Hint: you know several points on this function and you know what type of function it is.
Units(x) =
Now write a function for the revenue that the apartment manager makes as a function of x.
Revenue(x) =
Finally, Plot the revenue function and verify visually that there is a rent that can be charged that gives a maximum revenue.
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