# Demand, revenue, cost & profit

### Demand, revenue, cost & profit

#### Lessons

Demand is the relationship between the price of an item and the number of units that will sell at that price. In other words,
Demand →$p(q)$
where p is the price and q is the number of quantity. Usually, $p(q)$ is expressed as the equation
$p = mq+b$

Revenue is the amount of income a company makes. The revenue function is expressed as
$R=pq$
When you know what the demand is, then you can express $R$ as a function in terms of $q$.

Cost is the amount of money a company needs to produce the items they are selling. It is usually expressed as $C(q)$.

Profit is the net amount a company makes. It can be calculated by subtracting revenue from cost. In other words,
$P(q)=R(q)-C(q)$
• Introduction
Demand, Revenue, Cost & Profit Overview:
a)
Demand functions

b)
Revenue functions

c)
Cost functions

d)
Profit functions

• 1.
Finding the Demand, Revenue, Cost and Profit Functions
Desmond's Laptop Company is selling laptops at a price of $400 each. They estimate that they would be able to sell 200 units. For every$10 dollars increase in price, the demand for the laptops will decrease 30 units. Assume that the fixed cost of production is $42500 and each laptop costs$50 to produce.
a)
Find the demand function $p(q)$

b)
Find the revenue function $R=R(q)$

c)
Find the cost function $C=C(q)$

d)
Find the profit function $P(q)$. What is the net profit if 100 units are sold?

• 2.
Patsy is selling phones at a price of $700 each. They estimate that they would be able to sell 1000 units. For every$1 dollars decrease in price, the demand for the phones will increase by 50 units. Assume that the fixed costs of production are $300000 and each phone costs$200 to produce.
a)
Find the demand function $p(q)$

b)
Find the revenue function $R=R(q)$

c)
Find the cost function $C=C(q)$

d)
Find the profit function $P(q)$. For what values of $q$ will we have a negative net profit?

• 3.
Break even points
The demand and cost function for a certain company is:
$p=-q+400$
$C(q)=1000+19q^2$
For what value(s) of $q$ causes you to have a profit of zero?

• 4.
The demand and cost function for a certain company is:
$p=\frac{9}{q^2}$
$C(q)=6+3q$
For what value(s) of $q$ causes you to have a profit of zero?