Supply and demand. At a price of $ 2.28 per bushel, the supply of barley is 7,500 million bushels and the demand is 7,900 million bushels. At a price of $ 2.37 per bushel, the supply is 7,900 million bushels and the demand is 7,800 million bushels. (A) Find a price-supply equation of the form p = m x + b . (B) Find a price-demand equation of the form p = m x + b . (C) Find the equilibrium point. (D) Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system .
Supply and demand. At a price of $ 2.28 per bushel, the supply of barley is 7,500 million bushels and the demand is 7,900 million bushels. At a price of $ 2.37 per bushel, the supply is 7,900 million bushels and the demand is 7,800 million bushels. (A) Find a price-supply equation of the form p = m x + b . (B) Find a price-demand equation of the form p = m x + b . (C) Find the equilibrium point. (D) Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system .
Solution Summary: The author calculates the price-supply equation p=mx+b based on two points on the supply line.
Supply and demand. At a price of
$
2.28
per bushel, the supply of barley is 7,500 million bushels and the demand is 7,900 million bushels. At a price of
$
2.37
per bushel, the supply is 7,900 million bushels and the demand is 7,800 million bushels.
(A) Find a price-supply equation of the form
p
=
m
x
+
b
.
(B) Find a price-demand equation of the form
p
=
m
x
+
b
.
(C) Find the equilibrium point.
(D) Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system.
Formula Formula Point-slope equation: The point-slope equation of a line passing through the point (x 1 , y 1 ) with slope m , is given by the following formula: y - y 1 = m x - x 1 Example: The point-slope equation of a line passing through (2, -6) with slope 5 is given by: y - (-6) = 5(x - 2) y + 6 = 5(x - 2)
Calculate gross pay for each employee. All are paid overtime wage rates that are 1.5 times their respective regular wage rates. should be rounded to two decimal places at each calculation.
Taylor Series Approximation Example- H.W
More terms used implies better approximation
f(x) 4
f(x)
Zero order
f(x + 1) = f(x;)
First order
f(x; + 1) = f(x;) + f'(x;)h
1.0
Second order
0.5
True
f(x + 1) =
f(x) + f'(x)h +
ƒ"(x;)
h2
2!
f(x+1)
0
x; = 0
x+1 = 1
x
h
f(x)=0.1x4-0.15x³- 0.5x2 -0.25x + 1.2
51
Taylor Series Approximation H.w:
Smaller step size implies smaller error
Errors
f(x) +
f(x,)
Zero order
f(x,+ 1) = f(x)
First order
1.0
0.5
Reduced step size
Second order
True
f(x + 1) = f(x) + f'(x)h
f(x; + 1) = f(x) + f'(x)h + "(xi) h2
f(x,+1)
O
x₁ = 0
x+1=1
Using Taylor Series Expansion estimate f(1.35) with x0 =0.75 with 5
iterations (or & s= 5%) for
f(x)=0.1x 0.15x³-0.5x²- 0.25x + 1.2
52
Calculate gross pay for each employee. All are paid overtime wage rates that are 1.5 times their respective regular wage rates. should be rounded to two decimal places at each calculation.
Chapter 1 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
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