A farmer finds that if she plants 55 trees per acre, each tree will yield 25 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 4 bushels. How many trees should she plant per acre to maximize her harvest

31 trees per acre will maximize the harvest

Step-by-step explanation:

Given

trees/acre

bushels

Required

Number of trees to maximize harvest

From the question, we understand that:

Yield will decrease by 4 i.e. 25 - 4x

For every additional tree planted, i.e. 55 + x

So, the function is:

Open bracket

Rewrite as:

The maximum of a quadratic function is calculated as:

In the above equation:

So:

Recall that the number of trees to be planted is: 55 + x

So, we have:

Approximate

4

step-by-step explanation: