# An orchard contains 62 peach trees with each tree yielding an average of 50 peaches. For each 3 additional trees planted, the average yield per trees decreases by 12 peaches. How many trees should...

An orchard contains 62 peach trees with each tree yielding an average of 50 peaches. For each 3 additional trees planted, the average yield per trees decreases by 12 peaches. How many trees should be planted to maximize the total yield of the orchard?

the number of trees is=

Asked on by rmunoz90

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The orchard contains 62 peach trees with each tree yielding an average of 50 peaches. For each 3 additional trees planted, the average yield per trees decreases by 12 peaches.

If x sets of three extra trees are planted, the yield from the orchard is Y = (62 + 3x)*(50 - 12*3x) = -108*x^2-2082*x+3100

To determine the number of trees to be planted to maximize the yield solve Y' = 0 for x.

Y' = -216x - 2082

-216x - 2082 = 0

=> x = -1043/105

=> `x ~~ -10`

Assuming that as the number of trees is decreased there is an increase in the yield, the total number of trees in the orchard should be approximately 32. Else, the number of trees in the orchard should not be increased.

Planting extra trees decreases the total yield of the orchard.

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