(1) RELATED RATES. Provide all details as demonstrated in class. x= chronological order of the second letter in your first name y = is the last digit of your student number, example, 5 in 20x-12345. (a) DEMAND RATE When the price of a certain commodity is p dollars per unit, customers demand x hundred units of the commodity, where * + 3px + p? = 79. How fast is the demand x changing with respect to time when the price is $5 per unit and is decreasing at the rate of 30 cents per month? (b) MANUFACTURING At a certain factory, output Q is related to inputs u and v by the equation 2u +30 Q = 3u + (u + v)* If the current levels of input are u = 10 and v = 25, use calculus to estimate the change in input v that should be made to offset a decrease of 0.7 unit in input u so that output will be maintained at its current level.
(1) RELATED RATES. Provide all details as demonstrated in class. x= chronological order of the second letter in your first name y = is the last digit of your student number, example, 5 in 20x-12345. (a) DEMAND RATE When the price of a certain commodity is p dollars per unit, customers demand x hundred units of the commodity, where * + 3px + p? = 79. How fast is the demand x changing with respect to time when the price is $5 per unit and is decreasing at the rate of 30 cents per month? (b) MANUFACTURING At a certain factory, output Q is related to inputs u and v by the equation 2u +30 Q = 3u + (u + v)* If the current levels of input are u = 10 and v = 25, use calculus to estimate the change in input v that should be made to offset a decrease of 0.7 unit in input u so that output will be maintained at its current level.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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Transcribed Image Text:(1) RELATED RATES. Provide all details as demonstrated in class.
x= chronological order of the second letter in your first name
y = is the last digit of your student number; example, 5 in 20x-12345.
(a) DEMAND RATE When the price of a certain commodity is p dollars per unit,
customers demand x hundred units of the commodity, where
f + 3px + p² = 79.
How fast is the demand x changing with respect to time when the price is $5 per
unit and is decreasing at the rate of 30 cents per month?
(b) MANUFACTURING At a certain factory, output Q is related to inputs u and v by
the equation
2u + 30
Q = 3u? +
(u+v)
If the current levels of input are u = 10 and v =
change in input v that should be made to offset a decrease of 0.7 unit in input u so
that output will be maintained at its current level.
25, use calculus to estimate the
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