Thread: Algebra Word Problem-HELP!

I have been working on this math problem for days and can't seem to figure it out. My math book does not have any examples like this at all. I cannot figure out how to find a quadratic function for this information (I can only seem to find a linear equation). I typed the exact question below and if anyone can help or give any advice at all that would be great! Thanks.

You are given the task of estimating the number of trees that will maximize the fruit production per acre of a local orchard. By researching other local orchards you discover that at 400 trees per acre each tree will produce an average of 30 pounds of fruit. For each tree that is added to the acre, the average production per tree goes down 0.05 pounds.

a. Use the given info to build a table of values for this situation. Let t be the number of trees above 400 planted on an acre and find the total amount of fruit each acre will produce.

b. Find a function for the total production per acre when t trees over 400 are planted on one acre.

Originally Posted by vp1489

I have been working on this math problem for days and can't seem to figure it out. My math book does not have any examples like this at all. I cannot figure out how to find a quadratic function for this information (I can only seem to find a linear equation). I typed the exact question below and if anyone can help or give any advice at all that would be great! Thanks.

You are given the task of estimating the number of trees that will maximize the fruit production per acre of a local orchard. By researching other local orchards you discover that at 400 trees per acre each tree will produce an average of 30 pounds of fruit. For each tree that is added to the acre, the average production per tree goes down 0.05 pounds.

a. Use the given info to build a table of values for this situation. Let t be the number of trees above 400 planted on an acre and find the total amount of fruit each acre will produce.

b. Find a function for the total production per acre when t trees over 400 are planted on one acre.

Number of trees per acre = (400 + t).
Amount of fruit per tree = (30 - 0.05 t) pounds.

Amount of fruit per acre = (number of trees per acre)(amount of fruit per tree):

A = (400 + t)(30 - 0.05 t)

That is exactly the formula that I came up with, but here is the thing

1) This question (in my book) is in a "Quadratic Functions" chapter, so I am assuming that my function and graph need to be a parabola

2) If it asks me to find the number of trees that will maximize the fruit production, wouldn't I need to have a parabola (and not a line) to find that max number?

Thanks for the help!

Nevermind nevermind you did give me a quadratic equation! Thank you!

Originally Posted by mr fantastic

Number of trees per acre = (400 + t).
Amount of fruit per tree = (30 - 0.05 t) pounds.

Amount of fruit per acre = (number of trees per acre)(amount of fruit per tree):

A = (400 + t)(30 - 0.05 t)

Originally Posted by vp1489

That is exactly the formula that I came up with, but here is the thing

1) This question (in my book) is in a "Quadratic Functions" chapter, so I am assuming that my function and graph need to be a parabola

2) If it asks me to find the number of trees that will maximize the fruit production, wouldn't I need to have a parabola (and not a line) to find that max number?

Thanks for the help!

The function defining A is a parabola (an upside down parabola). Why do you think otherwise?

It cuts the t-axis at t = -400 and t = 600 ......

Okay now with that equation (400+t)(30-.05t) the number of fruit increases as I add additional numbers of trees....and the original problem says that for each tree that is added to the acre, the average production per tree goes down 0.05 pounds.

Im very confused as to why this happens.

Originally Posted by vp1489

Okay now with that equation (400+t)(30-.05t) the number of fruit increases as I add additional numbers of trees....and the original problem says that for each tree that is added to the acre, the average production per tree goes down 0.05 pounds.

Im very confused as to why this happens.

1. There is a difference between the amount of fruit per acre and amount of fruit per tree ...... More trees means more fruit (up to a point) but each tree is producing less fruit. You need to substitute values for t and see what's happening ......

2. It makes perfect sense that if you plant more trees per acre, each tree will produce less fruit ...... I would assume that when you plant more trees, there are less resources available to each tree for its growth. The logical result of this would be that each tree produces less fruit. Is that what's worrying you?

Originally Posted by mr fantastic

The function defining A is a parabola (an upside down parabola). Why do you think otherwise?

It cuts the t-axis at t = -400 and t = 600 ......

Because as I add more or less trees per acre the A increases and decreases in a linear manner not as a parabola.

Originally Posted by vp1489

Because as I add more or less trees per acre the A increases and decreases in a linear manner not as a parabola.

No. As you change t, the value of A does not change in a linear manner ..... Substitute some values of t and calculate the value of A. Plot the points. They do not lie on a line.