Equilibrium Point: find quadratic regression from table data

[Error_Analysis]

I'm stuck on a HW problem. I have the answer (I won't always have the answer - I just happened to look in the back of the book for help) in the first place - where I'm stuck is how to get to the answer. I understand how to do the workings upon a graphing calculator - but how to solve for the demand for a given price level is confusing.

1. A company is planning to introduce a ten-piece set of non-stick cookware. A marketing company established price-demand and price-supply tables for selected prices (Table 1 and Table 2), where x is the number of cookware sets people are wiling to buy and the company is willing to sell each month at a price of p dollars per set.

[As an FYI both tables require the same information, so I'm only putting Table 1 up, since if I understand Table 1, Table 2 should be easy to understand - just with a change in information.]

TABLE 1
x: 985, 2145, 2950, 4225, 5100
p= D(x)($) : 330, 225, 170, 105, 50

A. Find a quadratic regression model for the data in Table 1. Estimate the demand at a price level of $180.

So, after plugging all of that junk into my calculator I got the following answer for the regression equation:
ax^2 + bx + c

a = 5.94772121 E -6
b= -.1024018814
c= 422.3467853

Now, how do I find the demand for the given price - when the answer is 2,833?

I have tried plugging 180 for x, but that doesn't seem to work.

Help?

 

[mmm4444bot]

Re: Equilibrium Point

... [price level] p = D(x) [= {330, 225, 170, 105, 50}, where x = demand]

... Estimate the demand at a price level of $180.

... tried plugging 180 for x, but that doesn't seem to work.

To me, it looks like you need to use your quadratic model to determine a value for x which causes D(x) to equal 180, and then round this result to an integer.

Cheers,

~ Mark

 

[Error_Analysis]

Re: Equilibrium Point

That works very well. Thank you for your advice.

And stupidity struck me quite early - seeing as upon further inspection on my calculator, I've found a TRACE button, which after graphing it on a plane, can find the point in which D(x) = 180, and gives you the other coordinate - to a good estimation around the answer given.

But thank you very much.

 

[mmm4444bot]

Re: Equilibrium Point

... found a TRACE button, which ... gives ... a good estimation ...

As an alternative to estimating with TRACE, if your machine has a built-in equation solver or built-in quadratic formula, then you could use your machine to do all of the algebra in solving the quadratic equation, as opposed to using it only as a tool for doing the arithmetic.

Cheers,

~ Mark