Question

A new software company wants to start selling DVDs with their product. The manager notices that when the price for a DVD is 16 dollars, the company sells 150 units per week. When the price is 27 dollars, the number of DVDs sold decreases to 82 units per week. Answer the following questions:
(A) Assume that the demand curve is linear. Find the demand, q, as a function of price, p. (B) Write the revenue function, as a function of price. (C) Find the maximum revenue.

Answer 1

@amistre64 Hi! Can you help me again?

Answer 2

you have 2 points of reference, right?

Answer 3

(16,150) (27,82)

Answer 4

When I calculated the slope, I got -68/11

Answer 5

thats what the slope if between the points yes

Answer 6

f(p) = slope(p-po) + f(po)

Answer 7

I thought we were supposed to use q= mp + b ?

Answer 8

there is more than one form of a line, but if you must

m(p-po) + f(po) can be distributed and collected as mp+b

Answer 9

Well I ended up getting q=(-68/11)p + 249 but it said it is incorrect :/

Answer 10

And I don't know what I did wrong

Answer 11

-68/11(x-27)+82

2738/11-(68 x)/11

id say you mathed an error into it

Answer 12

if we know y=mx+b, then b=y-mx right?

82 + 68/11 (27) = b

Answer 13

248.9

Answer 14

But that's the same thing as 249 haha

Answer 15

.909090...

but yeah :)

Answer 16

now how do we determine revenue?

Answer 17

wait so why is q=(-68/11)p + 249 wrong? :/

Answer 18

becasue 249 is not right

Answer 19

keep it as a faction

Answer 20

or fraction even

Answer 21

q = (-68p+2738)/11

Answer 22

or

q = -(68p-2738)/11 either way to me

Answer 23

revenue is just price times quantity sold ... or pq

Answer 24

Ok got it! I just need help with part D :)

Answer 25

youll need to post part D

Answer 26

Oops sorry C

Answer 27

what is your quadratic from B?

Answer 28

q= -68/11p^2+248.9p

Answer 29

if you havent learned how to determine the min or max of a U shaped curve by now .. theres not much i can do to save you lol

Answer 30

Do you have to graph it?

Answer 31

you can, if you must

Answer 32

the min or max of a quadratic occurs at the middle of the roots ....

Answer 33

pq has roots when p=0, or q=0

Answer 34

what is the q intercept? then half it

Answer 35

or just do -b/(2a)

Answer 36

well, that is not the max, but that is where the max occurs

Answer 37

I got -20.13 but that's wrong

Answer 38

20.13 is the price that gets us the most revenue ... let p=20.13 ... what is the revenue from it?

Answer 39

strategy:

define the line q=mp+b from the points of reference

define the revenue as pq

determine the value of p, that gets us the most revenue

use that value to determine the max revenue