project: estimating trees for max per-acre production

[cpbush07]

I need help with this word problem... any suggestions...?

This is a Project that should be ideal for some fruitheads.

You have been selected to estimate the number of trees that will maximize the avocado production per acre for a local grower. By researching other orchards, you discover that at 400 trees per acre each tree will produce an average of 30 pounds of avocados. For each tree that is added to the acre, the average production per tree goes down 0.05 pounds.

Use the given information to build a table of values (I suggest that you increase from the base of 400 by at least 20 trees at a time). Let t be the number of trees above 400 planted per acre and find the total amount of fruit each acre will produce. Find at least 8 sets of values.

Create a scatter diagram and graph the information. This can be done very easily using a program such as Microsoft Excel.

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

Estimate how many trees should be planted (total) per acre to produce 12,400 pounds of avocados.

Find the number of trees that should be planted per acre to MAXIMIZE fruit production.

here's what i have so far:
let A= lbs of avocados produced

  t          A
  20       12579
  40       13178
  60       13777
  80       14376
 100       14975
 120       15574
 140       16173
 160       16772

 

[Denis]

Nobody should do YOUR project :shock:

However, so you don't keep going the wrong way, be advised that
your "8 sets of values" are NOT correct:
"For each tree that is added to the acre, the average production per
tree goes down 0.05 pounds."

This means .05 times the number of trees added : FOR EACH TREE.
So adding 20 trees means average becomes 30 - 20(.05) = 29;
420 * 29 = 12180 (not 12579; you're using average of 29.95 for all cases!)

Carry on, and good luck.

 

[cpbush07]

Thanks for the direction, which is what I was asking for- HELP with the problem, not answer my problem.q