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A demand function is a mathematical representation of the relationship between the quantity of a good that consumers are willing and able to purchase and the price of that good. Typically, demand decreases as price increases. This negative relationship means that the function generally has a downward slope.

For example, in the given exercise, the demand function is:

 \( D(p) = 7500 - 25p \)

Where:

•  \( D(p) \) represents the demand
•  \( p \) represents the price

This equation tells us that for every unit increase in price, the quantity demanded decreases by 25 units. Starting at a demand of 7500 units when the price is zero, the demand diminishes linearly as the price increases.

A supply function represents the relationship between the quantity of a good that producers are willing and able to sell and the price of that good. Usually, supply increases as price increases. This positive relationship means that the function typically has an upward slope.

In the exercise, the supply function is:

 \( S(p) = 6000 + 5p \)

Where:

•  \( S(p) \) represents the supply
•  \( p \) represents the price

According to this equation, for every unit increase in price, the quantity supplied increases by 5 units. Starting with a supply of 6000 units when the price is zero, the supply grows linearly as the price rises.

To find the equilibrium point in a market, you need to determine where the quantity demanded equals the quantity supplied. Mathematically, this is done by setting the demand function equal to the supply function and solving for the price.

For the given functions:
 \( 7500 - 25p = 6000 + 5p \)

We solve for the price by isolating \( p \):
 Combine like terms on each side:
 \( 7500 - 6000 = 25p + 5p \)

This simplifies to:
 \( 1500 = 30p \)

Next, divide both sides by 30:
 \( p = \frac{1500}{30} = 50 \)

Thus, the equilibrium price is \( 50 \).

To find the equilibrium quantity, substitute this price back into either the demand or supply function:
 Using the demand function:

 \( D(50) = 7500 - 25(50) = 6250 \)

Alternatively, using the supply function:
 \( S(50) = 6000 + 5(50) = 6250 \)

Both calculations confirm that the equilibrium quantity is 6250 units. Thus, the equilibrium point is \( (50, 6250) \).