The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $144. The quantity demanded each month is 1000 when the unit price is $114. The suppliers will market 700 espresso makers when the unit price is $66. At a unit price of $96, they are willing to market 2200 units. Both the supply and demand equations are known to be linear.
To find the linear demand equation, we need to calculate the slope and the y-intercept using the information provided.
Let's start by finding the slope (m):
We can use the formula for slope (m) which is:
m = (y2 - y1) / (x2 - x1)
Using the points (144, 250) and (114, 1000):
m = (1000 - 250) / (114 - 144)
m = 750 / -30
m = -25
So, the slope (m) is -25.
Next, let's find the y-intercept (b):
Using the point (144, 250):
250 = -25(144) + b
250 = -3600 + b
b = 250 + 3600
b = 3850
So, the y-intercept (b) is 3850.
Therefore, the linear demand equation is:
Quantity Demanded (x) = -25p + 3850
Now, let's find the linear supply equation.
Using the points (66, 700) and (96, 2200):
m = (2200 - 700) / (96 - 66)
m = 1500 / 30
m = 50
So, the slope (m) for supply is 50.
Using the point (66, 700):
700 = 50(66) + b
700 = 3300 + b
b = 700 - 3300
b = -2600
So, the y-intercept (b) for supply is -2600.
Therefore, the linear supply equation is:
Quantity Supplied (x) = 50p - 2600