Lanier review 51

Question

Supply & Demand

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

For a particular product, the supply equation isy=7x+517y=7x+517and the demand equation isy=−2x+688y=-2x+688

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

y = 7x + 517 and y = −2x + 688 but the intersection point occurs when the two x's are the same and the 2 y's are the same. If the y's are the same, and one y equals 7x + 517 and the other y equals −2x + 688, then 7x + 517 must equal −2x + 688.

7x + 517 = −2x + 688,

9x + 517 = 688

9x = 171

x = 19

If x = 19, then using y = 7x + 517, we can calculate y:

y = 7(19) + 517

y = 650

The intersection point is (19, 650)

Since the price of the item is x, the price is $19.00

Since the number of items is y, the amount of items in the market when supply and demand are in equilibrium is 650.

Answer 2

1) Read question.

2) x is price in dollars, y is number of items sold

3) Label supply equation in red, demand equation in blue.

4) Intersect the two equations using a graph to find equilibrium.

5) (19,650) is intersection, meaning x = $19, and y = 650 items sold.

6) Confirm setting 7x+517 = -2x+688

7) Solve to find x = 19

8) Substitute back into another equation to find y = 650.

Answer 3

This is a systems of equation question.

Since doth equations are solved for y the method here would be substitution.

Replace one of the y's with the other part of the equation such as

y= 7x+517

y=-2x+688

-2x+688=7x+517

Solve for x

688= 9x+517

191= 9x

x= 19

Remember that x was the price per item and the y was the number of items

The ordered pair is ( 19, 1167) You get the y in this ordered pair by substituting the 19 for the x in either equation and solving for y

Since this is the intersection point it is the equilibrium. so you need to sell at $19 / item and produce 1167 items.