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mathcalculus
 2 years ago
help: related rate problem with demand: (attached)
mathcalculus
 2 years ago
help: related rate problem with demand: (attached)

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mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i understand how to find dx/dt but im not so sure about part b) to find the revenue

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so my answer to a) idx/dt=100.

e.mccormick
 2 years ago
Best ResponseYou've already chosen the best response.0Demand is how many are sold. Revenue is income from the sales.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yes i know, but how does i figure it out for part b

e.mccormick
 2 years ago
Best ResponseYou've already chosen the best response.0So you solved for p and took the first derivative of that?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i have all my work attached

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.0revenue = price*quantity R = p*x but px = 50 by definition of demand function so revenue is constant at 50

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i tried putting that in but it doesnt work:/

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i also tried zero.

e.mccormick
 2 years ago
Best ResponseYou've already chosen the best response.0The rate at which 50 is changing is 0.

e.mccormick
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm... very odd. If it is not the derivative or the constant and they gave you nothing else....

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i tried 0 50 and it's wrong:/

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.0how did you get dx/dt = 100 ? if price is increasing , then quantity should be decreasing

e.mccormick
 2 years ago
Best ResponseYou've already chosen the best response.0I wonder if they mean Marginal Revenue: http://economics.about.com/od/production/ss/MarginalRevenueAndTheDemandCurve.htm

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1\[p \frac{ dx }{ dw }+x \frac{ dp }{ dw }=0\]. you can find the price based on the demand/price equation \[xp=50\] plug in what you know to find what you need.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i have it up there @pgpilot326

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1it seems as though the revenue is unchanged, holding constant at $50

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i mean, is the work right or wrong?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0then is part A? wrong?

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1as such the rate of change of revenue is $0.

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.0@mathcalculus , sorry didnt see you posted your work ok your work is good but seems you just plugged in wrong numbers x = 30 dp/dt = 0.5 p = 5/3 dx/dt = 9

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1where did the 100 come from?

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.0solving the equation you had 30(.5) + (5/3)dx/dt = 0

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0@dumbcow it's okay

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0@dumbcow im still not sure how 9 came from

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1x=30, p = 5/3, dp/dw = .5 and solve for dx/dw, yeah?

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1what? where did that come from? it says "when demand is 30"

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0and why can't we plug in dx/dt as 30 if dp/dt is 0.5

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1gx/dt is the change in demand relative to th echange in time

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so wouldn't it be 30?

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.0hmm, ok to get price of 5/3 you plugged in x=30 right

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.0so why would x change its value....if its 30 its 30 :)

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0so bc price is 0.5 to 1.67.... then we have a change?

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.0oh i see, there is a difference between current price and rate price is changing at this moment, x=30 and p=5/3 the rate they are changing is dp/dt = 0.5 , dx/dt = 9 so a week later the price will increase and quantity will decrease

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i tried. 30 as dx/dt

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i tried 0 and 50 for part b still wrong ::??

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.0in other words, you would never say the price is 0.5

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0okay can i see the answers to check if theyre right?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i kept trying everything, nothing works.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0(a) The rate at which the demand is changing is . (b) The rate at which the revenue is changing is .

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1the only thing I can think of is to write x as a function of p, i.e., \[x=\frac{ 50 }{ p }\] Then \[\frac{ dx }{ dt }=\frac{ 50 }{ p ^{2} }\times \frac{ dp }{ dt }\] See what that gets you...

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.0that gives you same thing.... dx/dt = 9

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.0as far as revenue, not sure what to do the rate has to be 0

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1revenue = price x quantity sold

pgpilot326
 2 years ago
Best ResponseYou've already chosen the best response.1Marginal revenue is equal to the ratio of the change in revenue for some change in quantity sold to that change in quantity sold. This can also be represented as a derivative when the change in quantity sold becomes arbitrarily small. More formally, define the revenue function to be the following \[ R(q)=P(q)\cdot q \]. By the product rule, marginal revenue is then given by \[ R'(q)=P(q) + P'(q)\cdot q\]. For a firm facing perfect competition, price does not change with quantity sold (P'(q)=0), so marginal revenue is equal to price.
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