For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price. 2x + 3p − 12 = 0 and 3x − 11p + 13 = 0 The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $132. The quantity demanded each month is 1000 when the unit price is $102. The suppliers will market 700 espresso makers when the unit price is $60. At a unit price of $90, they are willing to market 2200 units. Both the supply and demand equations are known to be linear. (a) Find the demand equation. p = (b) Find the supply equation. p = (c) Find the equilibrium quantity and the equilibrium price. Find the break-even point for the firm whose cost function C and revenue function R are given. C(x) = 14x + 28,000; R(x) = 21x (x, y) =
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price.
The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $132. The quantity demanded each month is 1000 when the unit price is $102. The suppliers will market 700 espresso makers when the unit price is $60. At a unit price of $90, they are willing to market 2200 units. Both the supply and demand equations are known to be linear.
(a) Find the demand equation.
p =
(b) Find the supply equation.
p =
(c) Find the equilibrium quantity and the equilibrium price.
Find the break-even point for the firm whose cost function C and revenue function R are given.
C(x) = 14x + 28,000; R(x) = 21x
(x, y) =
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