ssessment zainab hasan eek 10 Due in 1 hours, 30 minutes. Due Mon 06/11/2018 11:

Question

ssessment zainab hasan eek 10 Due in 1 hours, 30 minutes. Due Mon 06/11/2018 11:59 pm Show Intro/Instructions A farmer finds that if she plants 80 trees per acre, each tree will yield 30 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 2 bushels. How many trees should she plant per acre to maximize her harvest? Preview trees Give your answer rounded to the nearest whole number. License Points possible: 1 Unlimited attempts. Submit 1029 PM

Explanation / Answer

Here if x is the number of tree planted per acre and y is the number of bushels of fruit.

Total fruite yield when x = 80 is y = 30

so total bushels = 80 * 30 = 2400

Tota production = xy

here

if x is increased by k then y will decrese by 2k.

so total production

= (x + k) * (y - 2k)

= xy + ky - 2kx - 2k2

Here difference in production = xy + ky - 2kx -2k2 - xy = ky - 2kx -2k2

differention with k

y - 2x - 4k = 0

so here x = 80 and y = 30

30 - 2 * 80 - 4k = 0

4k = 30 - 160 = -130

k = -32.5

so here the optimum planted trees = 80 - 32.5 = 47.5

Optimum bushels per tree = 30 + 32.5 * 2 = 95

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