Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Ask your questions and receive precise answers from experienced professionals across different disciplines. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Answer:
a.)
Number of bushes = b = 129 + 4(7) = 129 + 28 = 157 bushes
b.)
Revenue = bx = (157)(31.4) = $ 4929.8
Step-by-step explanation:
Let number of bushes = b
The price of the bushes = x
The time to harvest = t
The revenue = y
Now given,
Price = x = 37 - (0.8)t
and
Number of bushes = b = 129 + 4t
Also,
The revenue = (Number of bushes)(Price of the bushes)
= bx
= (129 + 4t)[37 - (0.8)t]
= 129×37 - 129× (0.8)t + 4×37t - 4×0.8t²
= 4773 - 103.2t + 148t - 3.2t²
= 4773 + 44.8t - 3.2t²
⇒ y = 4773 + 44.8t - 3.2t²
Now,
[tex]\frac{dy}{dt}[/tex] = 0 + 44.8 - 6.4t
Now,
[tex]\frac{dy}{dt}[/tex] = 0
⇒ 44.8 - 6.4t = 0
⇒ - 6.4t = -44.8
⇒ 6.4t = 44.8
⇒t = [tex]\frac{44.8}{6.4} = 7[/tex]
Now,
[tex]\frac{d^{2}y }{dt^{2} }[/tex] = -6.4
As [tex]\frac{d^{2}y }{dt^{2} }[/tex] < 0 ,
It means at time t = 7 , the revenue is maximum
a.)
Number of bushes = b = 129 + 4(7) = 129 + 28 = 157 bushes
Price = x = 37 - (0.8)(7) = 37 - 5.6 = 31.4
b.)
Revenue = bx = (157)(31.4) = 4929.8
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.