Math 180 - Due Monday October 19 – SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES

In the MSC, the computers # 36, 38, 57, 58 have the TI CONNECT software and steps to paste a calculator screen onto your paper

NEATNESS REQUIRED – This paper needs to be typed.

Each year, the Harvey County Fair sets prices for concession vendors. The following table lists the data for supply and demand of a funnel cake at different prices.

Note:

L1 = prices of funnel cakes (in dollars)

L2 = Supply (in thousands of funnel cakes)

L3 = Demand (in thousands of funnel cakes)

Complete all of the following:

1) Use the calculator to construct a scatter-diagram for the supply and demand equations

Must turn ON two plots; one for the supply and another for the demand

2) Use the calculator to find the line of best fit for the demand and supply equations.

Paste one of them in Y1 and the other one in Y2. Write both functions using function notation D(p) and S(p). Use p instead of x and D or S instead of y. In each of the equations, LABEL the meaning of the variables using words and units

3) Do ZOOM 9 to show both lines along with both scatter-diagrams.

4) Use the calculator to find the equilibrium point.

5) The calculator screen showing both scatter-diagrams, the lines and the equilibrium point (with the x and y showing) has to be pasted into your word document. GO TO THE MATH SCIENCE CENTER and use TI-CONNECT to connect your calculator to the computer and PASTE in a word document.

6) Label the axes with words and units. Label the equilibrium point. (This can be done by hand)

7) Show how you find the equilibrium point algebraically. Interpret answer in words within context.

SOLUTION - Problem 46, page 259–Bittinger - Funnel Cakes

L1 = Price per unit ($)

L2 = Supply (thousands of funnel cakes)

L3 = Demand (thousands of funnel cakes)

Y1 is the Supply Function. It has a positive slope because at a higher price suppliers are willing to supply more funnel cakes

Y1 is the number of thousands of funnel cakes suppliedX is the price of each funnel cake

Y2 is the Demand Function. It has a negative slope because at a higher price, consumers buy less funnel cakes

Y2 is the number of thousands of funnel cakes demandedX is the price of each funnel cake

The point of intersection represents the EQUILIBRIUM POINT.

At that price, the amount that the seller will supply is the same amount that the consumer will buy.

Find the Equilibrium Point algebraically:

Supply = Demand
3.8 x – 1.82 = -1.44x + 7.64
5.24 x = 9.46
x = 1.805 ~ 1.81 dollars / If x = 1.805..., plug it back into either the supply or demand equation and get
y = 3.8(1.8053)-1.82 = 5.0403 thousand funnel cakes = 5,040 funnel cakes

EP($1.81 , 5.040 thousand funnel cakes)

5,040 funnel cakes will be supplied and demanded when the price of each funnel cake is $1.81.