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 280 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 = ( 280 - 2x )

Explanation / Answer

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

Number of Plants =( 40 + x )

Output Per Plant = ( 280 - 2x )

Production = Number of Watermelon Plants * Output Per Plant

= (40+x) (280 - 2x)

dP/dx = (280 - 2x) - 2 = 278 - 2x

278 - 2x = 0

x = 278 / 2 = 139

No of additional plants = 139

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