A farmer grows a particular plant that has a gene that can be manipulated to con

Question

A farmer grows a particular plant that has a gene that can be manipulated to control the age t at which the plant matures. The number of seeds S(t) produced by a plant maturing at age t is S(f) = -0.1 t^2 + 50 t + 0.8 seeds per mature plant A farmer asks the geneticists to genetically engineer a plant line that accounts for the fact that on his farm, only P(t) = 70000/2 t + 100 plants mature to age t. What age of maturity should the geneticist select for the plants to maximize the seed production of the farmer's crop?. Between 90 and 100 days Between 110 and 120 days Between 120 and 130 days Between 100 and 110 days

Explanation / Answer

the no.s of seeds s(t) produced by plant maturing at age t is

s(t)==0.1t2+50t+0.8

s'(t)=0.2t+50=>s'(t)=0=>0.2t=-50 or t=250

p(t)=70000/2t+100

p(t)=116.67

the age of maturity between 110 and 120 days

(b.)

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