Demand, revenue, cost & profit  Derivative Applications
Demand, revenue, cost & profit
Related concepts:
 Consumer and producer surplus
Lessons
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,
$P(q)=R(q)C(q)$

1.
Demand, Revenue, Cost & Profit Overview:

2.
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. 
3.
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.