If someone could help me with these two questions it would b

If someone could help me with these two questions it would be greatly appreciated.

Thanks in advance!!

You can sell 100 pet chias per week if they are marked at $1 each, but only 90 each week if they are marked at $2/chia. Your chia supplier is prepared to sell you 30 chias each week if they are marked at $1/chia, and 70 each week if they are marked at $2 per chia. Write down the associated linear demand and supply functions. demand function q(rho) = supply function q(rho) = At what price should the chias be marked so that there is neither a surplus nor a shortage of chias? Find a linear equation whose graph is the straight line with the given properties. Through (24,-3.1) and increasing at a rate of 6 units of y per unit of x. y(x) =

Solution

a) The quantity functions q(p) you are told are linear so they must be of the form
q(p) = mp+c, for some values m and c which we have to determine.
Demand function : ( $1, 100) and ( $2 , 90)

slopem = ( 90 -100)/( 2-1) =-10 ; q = -10p +c

100 = -10 +c ---> c=110

So, q(p) = -10p +110

Supply function: ( 1, 30) and ( 2, 70)

slope m = ( 70 -30)/( 2-1) = 40

q(p) = 40p +c

30 = 40 +c ----> c= -10

q(p) = 40p -10

b)  nether surplus nor shortage occurs when demand = supply

-10p +110 = 40p -10

50p = 120

p = 24 chias