Question

Your market research shows that you can sell 250 pairs of sunglasses per week at $25 and 175 pairs of sunglasses pe week at $40. Your supplier will sell you 140 pairs if your sale price is $20 and they are prepared to sell you 390 pairs at $45. Write the associated linear supply and demand functions and find the equilibrium price. I come up with a negative dollar amount so I'm unsure what I've done wrong. Can anyone help?

Answer 1

can you type up your work? or show it on a file attachment?

Answer 2

for change in +15 dollars, the number of items sold changes by -75; thats a linear slope of -75/15 = -15/3 = -5

for change in +25 dollars, the number of items supplied changes by +250; thats a linear slope of 250/25 = 10/1 = 10

so far so good?

Answer 3

At the -75/15 I divided and got M=5. No?

Answer 4

Should be -5

Answer 5

D(x) = -5x +5(25) + 250
= -5x +375

S(x) = 10x -10(20)+140
= 10x - 60

if i see it right

Answer 6

-5x +375 = 10x - 60
+5x + 60 +5x +60
--------------------
435 = 15x
/15 /15
-----------
29 = x

Answer 7

http://www.wolframalpha.com/input/?i=%28y%3D-5x%2B375%29+and+%28y%3D10x+-+60%29

these are some odd equations :)

Answer 8

x = price, so at a price of 29 dollars, this equilibs to a quantity of 230

Answer 9

You're a life saver. Thank you so much!

Answer 10

youre welcome :)