For the supply equations, where X is the quantity supplied in units of a thousand and P is the unit price in dollars, (A.)- sketch the supply curve and (B.)- determine the price at which the supplier will make 2000 units of the commodity available in the market.
P= x^2 + 16x + 40
**Please help me! I have tried to figure this out using the supply = demand way but I cannot figure it out!
I tried to factor it also, but there is no way it can. My graph did not match up with the Y-intercept either. I am so lost!
This is not a supply = demand problem. You are given the relationshup between supply (x) and price (P).
The supply (in units of 1000) is x = 2.
The corresponding price is
P = 2^2 + 16*2 + 40 = 76
P can also be written
P = (x + 8)^2 - 24
but is meaningful for positive x only.
That may help you when plotting a graph of P(x).
To sketch the supply curve, we should first understand the relationship between quantity supplied (X) and unit price (P) given by the supply equation P = X^2 + 16X + 40.
To find the price at which the supplier will make 2000 units of the commodity available in the market, we can set X equal to 2000 in the supply equation and solve for P.
Let's solve these step by step:
A. Sketching the supply curve:
To sketch the supply curve, we need to plot multiple points on the graph, where each point represents a combination of X and P values. By connecting these points, we can then draw the supply curve.
We can start by arbitrarily selecting a few values for X and calculate the corresponding P values using the supply equation.
Let's choose X = 0, 10, and 20:
For X = 0, P = (0^2) + (16 * 0) + 40 = 40
For X = 10, P = (10^2) + (16 * 10) + 40 = 200
For X = 20, P = (20^2) + (16 * 20) + 40 = 520
Plotting these points on a graph (with X on the x-axis and P on the y-axis), we can see a general pattern emerging. Connecting these points will give us the shape of the supply curve. It might not be a straight line since the equation is quadratic.
B. Determining the price at which the supplier will make 2000 units available:
To find the price at which the supplier will make 2000 units available, substitute X = 2000 into the supply equation and solve for P.
P = (2000^2) + (16 * 2000) + 40 = 4,008,040
Therefore, the supplier will make 2000 units of the commodity available in the market at a price of $4,008,040.
Note: It's important to consider that this equation provides a simplified representation of the supply relationship and may not accurately reflect real-world conditions. Also, keep in mind that supply and demand interactions can shape market prices, and this equation only provides the supply side.