%3Ch3%20class%3D%22txt-hdr-sec%22%3EPlease%20use%20calculus%20principles%20to%20

Question

%3Ch3%20class%3D%22txt-hdr-sec%22%3EPlease%20use%20calculus%20principles%20to%20solve%0Athis%20problem%3A%3Cbr%20%2F%3E%3C%2Fh3%3E%0A%3Cp%3E%3Cstrong%3EA%20picture%20would%20be%20great!%3C%2Fstrong%3E%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3E%3Cstrong%3EThere%20are%2038%20apple%20trees%20in%20archard.%20Each%20tree%20produces%0A750%20apples.%20For%20each%20additional%20tree%20planted%20in%20the%20orchard%2C%20the%0Aapple%20output%20per%20tree%20drops%20by%208%20apples.%20How%20many%20additional%20trees%0Ashould%20be%20planted%20in%20the%20existing%20orchard%20in%20order%20to%20maximize%20the%0Aapple%20output%20of%20the%20orchard%3F%3Cbr%20%2F%3E%3C%2Fstrong%3E%3C%2Fp%3E%0A

Explanation / Answer

Let additional number of trees be x

Current Apple ouput per tree=750

Apple Output when x additional trees are planted= (750-8x)

Total Apple Ouput = (38+x)*(750-8x)=28500+750x-304x-8x^2=28500+446x-8x^2

d(Ouput)/dx=0

16x-446=0

x=27.875 number of additional tree should be planted

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