1.The manager of a 100-unit apartment complex knows from experience that all units will be occupied if the rent is $400 per month. A market survey suggests that, on the average, one additional unit will remain vacant for each $5 increase in rent. What rent should the manager charge to maximize revenue?
2.During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for $10 each and his sales averaged 20 per day. When he increased the price by $1, he found that he lost two sales per day.
a. Find the demand function, assuming it is linear.
b. If the material for each necklace costs Terry $6, what should the selling price be to maximize his profit?
Hi Jackie,
I can help get you started on the first problem.
You want to maximize the revenue so you need an expression for the revenue.
revenue = (number of units rented)
(rent per unit)
If the rent is set at $400 then all 100 units can be rented and the revenue would be
100
The manager is considering increasing the rent in increments of $5, but for each increment the number of units rented decreases by 1.
Suppose the decision is to increase the rent by x increments. The number of units rented would then be 100 - x and the rent per unit would be $400 + $5x. Hence the revenue would be
(100 - x)($400 + $5x)
This is the expression you need to maximize.
Penny