## soccergal12 3 years ago 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

1. javawarrior

isnt it just R(50) - 25*50 ?

2. soccergal12

so it would be 2500 ?

3. javawarrior

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

4. javawarrior

im getting 7500 not 2500, double check your working

5. ganeshie8

you should get 0. u still stuck ?

6. soccergal12

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

7. soccergal12

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

8. ganeshie8

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

9. soccergal12

yeah, it's asking for marginal profit

10. soccergal12

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

11. ganeshie8

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

12. soccergal12

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?

13. ganeshie8

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 }

14. ganeshie8

25x is you cost function

15. soccergal12

thank you!