Homework Help: pre-calc

Posted by Amanda on Monday, November 5, 2007 at 5:56pm.

If Wesley Jackson harvests his apple crop now, the yield will average 120 pounds per tree. Also, he will be able to sell the apples for $0.48 per pound. However, he knows that if he waits, his yield will increase by about 10 pounds per week, while the selling price will decrease by $0.03 per pound per week.

a. How many weeks should Mr. Jackson wait in order to maximize the profit?
b. What is the maximum profit?

How do you write an equation to represent all of this and lead you to your answer?

pre-calc - DrBob222, Monday, November 5, 2007 at 8:59pm
I presume that the 10 lbs increase each week is per tree; otherwise we need the number of trees.
You can make a table for one tree.

lbs.....price/lb....week...total price
120..... 0.48 ...... now .. 57.60
130..... 0.45 ....... 1 ... 58.50
140..... 0.42 ....... 2 ... 58.80
150..... 0.39 ....... 3 ... 58.50
160..... 0.36 ....... 4 ... 57.60

Here is the way I would do the equation.
Y = # weeks
120 + 10Y = # lbs apples available.
selling price is 0.48-0.03Y
# lbs apples available x selling price is total price Mr. Jackson obtains.
(120+10Y)(0.48-0.03Y)=selling price (s.p.) each week.
57.60 + 1.20Y -0.3Y² =s.p.
You can try week 1,2,3,and 4 and see what the selling price is.
I did that and obtained
now......57.60
week 1...58.50
week 2...58.80
week 3...58.50
week 4...57.60
Check my thinking. Check my work.

Answer this Question

Related Questions

Pre-Calculus - A farmer can plant a combination of two different crops on 20 ...
Algebra 2 - An orange grower finds that she can get an average yield of 40 ...
Algebra 2 - An orange grower finds that she gets an average yield of 40 bushels ...
business calculas - An apple orchard has an average yield of 38 bushels of ...
Statistics - What price do farmers get for their watermelon crops? In the third...
5th grade - Mike and Shannon harvested 110,793 pounds of winter wheat off of the...
physics - Maria throws an apple vertically upward from a height of 1.2 m with an...
physics - Maria throws an apple vertically upward from a height of 1.3 m with an...
algebra - walnuts that sell for $3 a pound and macadamia nuts that sell for $4 ...
Calculus - (a) If a farmer plants x units of wheat in his field, 0 ≤ x...

For Further Reading

First Name:
School Subject:
Answer: