Help me figure this one out!!!

[wmosley]

For a certain commodity, the demand equation is given by D= -5p + 5=. At a price of $1, twelve units of the commodity are supplied. If the supply equation is linear and the market price is $4, find the supply equation.

Answer:

For this one I have come up with a formula of:

s= ap+b where p if the varialbe, price, and a,b are constants

s is supply.

I think I have to find a and b but amd not sure.

Can someone help me with figure this one out...

[HallsofIvy]

Yes, since you are told that the supply equation is linear, it must be of the form
s= ap+ b. Further, you are told that "At a price of $1, twelve units of the commodity are supplied"- that is, when p= 1, s= 12 so 12= a(1)+ b or a+ b= 1. That means that b= 1- a and the supply equation can be written s= ap+ 1- a. Finally, you are told that the "Market price is $4" which means that the value of p at which the supply and demand equations give s= D is 4. The demand equation is D= -5p + 5. When p= 4, what is D? Now that you know D, you also know s: s= D. Put that value of s as well as p= 4 into the supply equation and solve for a.