You are here:

Calculus/Optimization Problems


An apple grower knows that the current yield per tree is 130 lbs, and the current price is $.73 per pound. Find the maximum revenue possible if the yield increases 5 pounds per week, and the price decreases 2 cents per week.

The changes in the amount of apples and the price is 130 + 5x and 73 - 2x,
where the money is kept in the number of pennies involved.

The amount of money is the amount produced times the sale price.
That makes it (130+5x)(73-2x).  Multiplying them out gives 9490 + 365x - 260x - 10x.
It is customary to put the highest power of x first and combine like terms.
This gives -10x + 105x + 9490.

If f(x) = -10x + 105x + 9490, then f'(x) = -20x + 105.
Setting this equal to 0 gives -20x + 105 = 0, so 20x = 105, so x = 105/20.

Now 105 and 20 are both divisible by 5, so that is x = 21/4.
To make this a proper fraction, that is x = 5 1/4.


All Answers

Answers by Expert:

Ask Experts




Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology (reproduction, insusion of chemicals into bloodstream).


Experience in the area: I have tutored students in all areas of mathematics since 1980. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Maybe not a publication, but I have respond to well oveer 8,500 questions on the PC. Well over 2,000 of them have been in calculus.

I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few courses at college a year early.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2017 All rights reserved.

[an error occurred while processing this directive]