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

Question

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) =

Explanation / Answer

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

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