# Demand, revenue, cost & profit #### Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered. #### Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals. #### Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now! ##### Intros
###### Lessons
1. Demand, Revenue, Cost & Profit Overview:
2. Demand functions
3. Revenue functions
4. Cost functions
5. Profit functions
##### Examples
###### Lessons
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.
1. Find the demand function $p(q)$
2. Find the revenue function $R=R(q)$
3. Find the cost function $C=C(q)$
4. 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.
1. Find the demand function $p(q)$
2. Find the revenue function $R=R(q)$
3. Find the cost function $C=C(q)$
4. 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?
1. 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?
###### Topic Notes
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,
$P(q)=R(q)-C(q)$