You have a garden row of 20 watermelon plants that produce an average of 30 watermelons apiece. For any additional watermelon plants planted, the output per watermelon plant drops by one watermelon. How many extra watermelon plants should you plant?

You should plant 5 extra watermelon plants to maximize production.

Since you have a garden row of 20 watermelon plants that produce an average of 30 watermelons a piece, and for any additional watermelon plants planted, the output per watermelon plant drops by one watermelon, to determine how many extra watermelon plants should you plant you must perform the following calculation:

Therefore, you should plant 5 extra watermelon plants to maximize production.

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You should plant another 25 watermelons.

Step-by-step explanation:

The total number of watermelons can be calculated as:

W = (20 + x)*(30 - x)

x is the number of plants that we add, for each plant that we add, the output per watermelon plants drops by one watermelon, then if we add x plants, each plant will give (30 - x) watermelons.

We want to maximize this equation, so let's distribute the product.

W = 600 + 30*x + 20*x - x^2

W = 600 + 50*x - x^2

Notice that this is a quadratic equation with a negative leading coefficient, this means that the maximum is at the vertex, and the arms of the equation will open down.

To find the maximum, we can just derive with respect to x, and find the value of x that makes that equal to zero, this is:

W'(x) = dW/dx = 50  - 2*x

W'(x) = 0 = 50 - 2*x

           2*x = 50

          x = 50/2 = 25.

Then the maximum output will be if you plant 25 more watermelon plants.

And this will be:

W(25) = 600 + 50*25 - 25^2 = 1,225 watermelons

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