Last year I planted 40 watermelon plants in my garden. On average each plant pro

Question

Last year I planted 40 watermelon plants in my garden. On average each plant produced 290 pounds of watermelons.

I have a limited amount of water that is used for irrigation. Because of this, for each additional plant added to the garden, the output per plant drops by 2 pounds.

I would like to increase the number of plants in my garden, but I am concerned that if I plant too many, that overall production will drop.

How many additional plants should I plant this year in order to maximize the total watermelon output of my garden?

Production = Number of Watermelon Plants * Output Per Plant

Hint:

   Let x = The Number of Plants that will be added to my gaden.

   Number of Plants =( 40 + x )

   Output Per Plant = ( 290 - 2x )

Explanation / Answer

Production = Number of Watermelon Plants * Output Per Plant

Production (P) = ( 40 + x ) * ( 290 - 2x )

P = -2x^2 + 210x + 11600

Now, differentiate P with respect to x, to find the maxima

P' = -4x + 210 = 0

-4x + 210 = 0

x = 52.5 watermelons ~ 52 watermelons

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