Question

The price p and the quantity x sold of a certain product obey the demand equation
x=-20p+500, 0≤p≤25
a.Express the revenue R as a function of x. (Hint: R = xp, where p is the unit price.)
b.What is the revenue if 20 units are sold?
c.How many of this item should be sold in order to get maximum revenue?
d.What is the maximum revenue?
e.The marginal revenue.
f.The marginal revenue at x = 100
@dumbcow

Answer 1

for a) revenue needs to be function of "x" so you need to solve the demand equation for "p"

Answer 2

yes how do i go about it,

Answer 3

algebra...move things to other side of equal sign until "p" is isolated
-subtract 500
-divide by -20

Answer 4

im ot -1x/20 +25/10 is it right?

Answer 5

got

Answer 6

oh wait a min

Answer 7

x/20-25 is what i got

Answer 8

you almost have it....-x/20 + 25

Answer 9

wait you changed the signs haha, you had it right before

Answer 10

lol.im figuring out where the mistake is from

Answer 11

ok got it now..wat do i do next

Answer 12

multiply that by "x" to get revenue

R(x) = x*p(x)

Answer 13

where x=-20p + 500 ??

Answer 14

or where x is x? lol

Answer 15

haha x is x
p = -x/20 + 25

Answer 16

so that means the demand equation where x= -20p +500 is no longer to be used in question a?

Answer 17

therefore R(x) =-1x^2/20+25x right

Answer 18

correct , its still the demand equation we just changed how it looked so everything is in terms of "x" not "p"

Answer 19

ok.so my R(X) IS -1x^2/20+25x

Answer 20

yep, part b) plug in x=20 to find revenue

Answer 21

IN THE R FUNCTION WE GOT?

Answer 22

@dumbcow

Answer 23

yeah thats revenue

Answer 24

oh ok..

Answer 25

i got 480

Answer 26

yep

Answer 27

is c asking for the vertex?

Answer 28

to get max revenue, set derivative equal to 0

yes find the vertex, but since you know calculus i would just take derivative

Answer 29

ok let me work it out and tell you what i got now

Answer 30

is 250 the answer

Answer 31

very good...then for part d) just plug that (x=250) into revenue function

Answer 32

ok a sec

Answer 33

i had 5937.5 is it right?

Answer 34

ok i got it now

Answer 35

i dont have to get a decimal

Answer 36

i get 3125

Answer 37

yes 3125

Answer 38

made a childish mistake earlier..llol

Answer 39

lol no problem
part e) is easy its just the derivative you did earlier

Answer 40

ok let me work it out.

Answer 41

-2x +25 ?

Answer 42

oops not again i omiiitted the 20

Answer 43

-x/10 +25 right

Answer 44

and f) is
15

Answer 45

@dumbcow

Answer 46

sorry correct on both :)

Answer 47

oh no need for sorry.

Answer 48

and my last question .i told u i got two lol