Question

You are given a pair of equations, one representing a supply curve and the other representing a demand curve, where p is the unit price for x items.
20p+x-276=0 and 84p-x-36=0
a. Domain of the supply curve=?
Domain of the demand curve=?
b. Determine the market equilibrium.
Equilibrium: x = p =
c. Determine the revenue function.
Revenue function R(x)=
d. Determine the revenue at market equilibrium.

Answer 1

hint: since you cannot have a negative price or a negative number of items, this means that both x and p are nonnegative numbers (ie they aren't negative)

Answer 2

so I recommend graphing 20p+x-276=0 on the xy plane (replace p with y) and only focusing on the first quadrant where x and y are both positive

Answer 3

this will help you determine the domain of 20p+x-276=0

Answer 4

so i graphed p=(-1/20)x+13.8 is that correct?

Answer 5

good, that's what you should get when solving 20p+x-276=0 for p

Answer 6

okay. and then the other equation is p=(1/84)x+(3/7) this one is the supply and the other equation is the demand. how do i find the domain of each?

Answer 7

good

Answer 8

to find the domain of p=(-1/20)x+13.8, you graph this equation

then determine what values of x are part of points that lie in the first quadrant

Answer 9

remember, x and p are either 0 or they are positive numbers

they are NEVER negative

Answer 10

so I recommend you finding the x and y intercepts because they can be used to figure out where the line crosses through the first quadrant (if it does at all)

Answer 11

for instance, here is a blank xy axis

Answer 12

and here is some demand line (this may or may not be your demand equation, it's just an example)

Answer 13

the x-intercept is 276 and the y intercept is 13.8 right?

Answer 14

the x and y intercepts points are marked