Question

Sarah's flower shop gets very busy on V-day, but they don't always sell out. Sarah knows that she can sell 50 rose bouquets at a price of $75 each, but she can sell 60 if she drops the price down to $65 each.
(a) find the demand function p(x) .. assume it's linear.
(b) find the revenue function R(x).
(c) find for which value(s) of x the marginal revenue equals to 0
(d) suppose each bouquet costs Sarah $25 to make. find the marginal profit for x = 50. what does this value mean?
I found the demand function : p(x) = -x + 125
And the Revenue function : R(x) = -x^2 + 125x
and found the marginal revnue: x = 125/2 rose bouquets
i don't get how to do part d

Answer 1

isnt it just

R(50) - 25*50 ?

Answer 2

so it would be 2500 ?

Answer 3

yep if marginal profit is total revenue - cost of making it

Answer 4

im getting 7500 not 2500, double check your working

Answer 5

you should get 0.

u still stuck ?

Answer 6

i got 7500, not zero. i put ((-50)^2 + 125(5)) - 25(50) in my calculator to get 7500.

Answer 7

i mean ((-50)^2 + 125(50)) - 25(50)

Answer 8

what you computing is overall profit. in the question they are asking about marginal profit right ?

Answer 9

yeah, it's asking for marginal profit

Answer 10

does that mean, it should be dP/dt = dR/dt - dC/dt ?

Answer 11

exactly.. you are correct.
marginal something means, derivative something

Answer 12

okay, i used the original profit function: p(x) -x +125 to get the derivative: p^1(x) = -1 ; so from this function, we know that the marginal profit is zero ? because you cannot plug in 50 for x, because there is no x variable in the derivative?

Answer 13

dP/dt = dR/dt - dC/dt

your above equation is right.
just take: (derivative of REVENUE) - (derivative of COST)

that comes like :
d/dx { R(x) } - d/dx { 25x }

Answer 14

25x is you cost function

Answer 15

thank you!