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Question 1197816: At a price of $4.96 per pound, the supply for cherries is 16,171 pounds, and the demand is 10,107 pounds. When the price drops to $4.14 per pound, the supply decreases to 10,590 pounds and the demand increases to 12,913 pounds. Assume that the price-supply and price-demand equations are linear.
What is the equilibrium quantity? Round to the nearest pound.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! linear equation is y = mx + b.
m is the slope.
b is the y-intercept, which is the value of y when x = 0.
at a price of 4.96 per pound, the supply is 16,171 pounds and the demand is 10,107 pounds.
at a price of 4.14 per pound, the supply decreases to 10,590 pounds and the demand increases to 12,913 pounds.
let x = the price per pound.
you have a demand equation and a supply equation.
the demand equation becomes:
y = -3421.95122 * x + 27079.87805
the supply equation becomes:
y = 6806.097561 * x -17587.2439
the intersection point is when the demand equation is equal to the supply equation.
this occurs when -3421.95122 * x + 27079.87805 = 6806.097561 * x - 17587.2439.
add 3421.95122 * x to both sides of the equation and add 17587.2439 to both sides of the equation to get:
27079.87805 + 17587.2439 = 6806.097561 * x + 3421.95122 * x
combine like terms to get:
44667.12195 = 10228.04878 * s
solve for x to get:
x = 4.367120544.
at that value of x, the demand = 12135.80458 and the supply = the same.
that's your equilibrium point.
your x value in both equations is the price per pound.
if you need further clarification as to how i got this answer, let me know and i'll supply you with the specifics on how the equations were derived.
it is, however a standard procedure on how to find the slope and the y-intercept of each equation.
the graph of the equations and the intersection point is shown below:
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