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(a) Determine if the given equation is a supply or demand equation. For a supply equation, find the minimum price for which there will be any supply. For a demand equation, find the maximum possible demand and the maximum price that can be charged. (b) Plot the graph of the given equation.$$2 p+x-12=0$$

(a) Demand, $x=12, p=6$

Algebra

Chapter 1

Functions and their Applications

Section 6

Economic Functions

Functions

McMaster University

Harvey Mudd College

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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(a) Determine if the given…

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working in terms of economic functions here were given to P plus x minus 12 is equal to zero. And what we would like to find is whether or not this is a supply or demand function. And then depending on that, we may want to find the minimum price or the maximum price and demand and then we're gonna graph it so it's going back to the function to P plus x minus 12 is equal to zero to determine if this is supply or demand. Let's solve for P. Because we know that both supply and demand are going to be a function of price. So starting to get p by itself, we can work our way down so we have to pee will be equal to let's subtract X from both sides and add 12. Now we can just divide both sides by two so that we have P. Is equal to negative one half X plus six. So what's key to looking at here right now is really just the sign of our slope because we know that demand curves are downward sloping while, as supply curves are upward sloping. So because we have this negative slope, we can say that this is a demand curve. Then we want to graph it and find the maximum price and demand for this curve. So we know it's going to be downward sloping. So let's give ourselves a downward sloping demand curve might look something like that. And if we want to find, let's start with this max price and locating the max price on the graph, it's going to sit up here, right? Because that's the highest point on this Y axis, on that price axis. And that point occurs when our X axis is equal to zero. So let's go ahead and plug in zero for X. So down here where we have quantity in this case, it's also X. So, plugging in zero for X. We have P is equal to negative one half time, zero plus six. So calculating this at what we see is that P then is equal to just six because those are going to cancel. So our maximum price that could be charged is $6. Now, if we wanted to know the maximum demand, that's otherwise known as this maximum quantity. So our maximum demand occurs at the point where it occurs down here. Right? That's when the quantity is the greatest or in other terms, that's when the price is equal to zero. So plugging those values and then we have for price that zero instead which is equal to negative one half X plus six. We need to solve for X. So we have negative six. Then by subtracting six from both sides is equal to negative one half, X Dividing both sides by negative one half. We see that our maximum demand then is when X is equal to 12.

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