In supply (and demand) problems,

Question

In supply (and demand) problems, y is the number of items the supplier will produce (or the public will buy) if the price of the item is x.

For a particular product, the supply equation isy=9x+432y=9x+432and the demand equation is y=−2x+729 y=-2x+729

What is the intersection point of these two lines?

     

Enter answer as an ordered pair (don't forget the parentheses).

What is the selling price when supply and demand are in equilibrium?

price = $/item

What is the amount of items in the market when supply and demand are in equilibrium?

number of items = 

Answer 1

The intersection point of two lines is where their "x" values are the same and where their "y" values are the same.

If one equation is:

y = 9x + 432

And the other equation is

y = −2x + 729

And their "y" values are the same, then "9x + 432" must be equal to "−2x + 729"

9x + 432 = −2x + 729 now add 2x to both sides to get:

11x + 432 = 729 then subtract 432 from both sides to get:

11x = 297 then divide both sides by 11 to get:

x = 27

To find the value of "y", pick either equation and plug in x = 27:

y = 9(27) + 432

y = 243 + 432

y = 675

So the intersection point is (27, 675)

Since you are told that y is the number of items the supplier will produce (or the public will buy), then the number of products is 675.

Since you are told that x is the price (we will have to assume the price is in dollars), then the price (when 675 items are sold) is $27

These are the number of items and the price when supply and demand are in equilibrium.