Solve problem (See Relating Concepts Exercise 1.)Harvesting a Cherry Orchard The manager o...

Solve problem (See Relating Concepts Exercise 1.)

Harvesting a Cherry Orchard The manager of a cherry orchard is trying to decide when to schedule the annual harvest. If the cherries are picked now, the average yield per tree will be 100 lb, and the cherries can be sold for 40 cents per pound. Past experience shows that the yield per tree will increase about 5 lb per week, while the price will decrease about 2 cents per pound per week. How many weeks should the manager wait to get an average revenue of $38.40 per tree?

Exercise 1

For individual or collaborative investigation

If p units of an item are sold for x dollars per unit, the revenue is px. Use this idea to analyze the following problem, working Exercise 2in order.

Number of Apartments Rented The manager of an 80-unit apartment complex knows from experience that at a rent of $300, all the units will be full. On the average, one additional unit will remain vacant for each $20 increase in rent over $300. Furthermore, the manager must keep at least 30 units rented due to other financial considerations. Currently, the revenue from the complex is $35,000. How many apartments are rented?

Exercise 2

Solve the equation from Exercise 3 and answer the question in the problem.

Exercise 3

According to the problem, the revenue currently generated is $35,000. Write a quadratic equation in standard form using your expression from Exercise 4.

Exercise 4

Use the answers in Exercise 5 and 6 to write an expression that defines the revenue generated when there are x increases of $20 over $300.

Exercise 5

Suppose that x represents the number of $20 increases over $300. Represent the number of apartment units that will be rented in terms of x.

Exercise 6

Represent the rent per unit in terms of x.