 Hello and welcome to the session. In this session we are going to discuss functions related to business and economics. And first we have cost function. The total cost of producing X unit of a commodity is denoted by a function to be equal to C of X explicitly f of C X is 0 in the implicit form and is called the cost function or total cost function. It consists of two parts. One is fixed cost. It is independent of the quantity produced that is it does not change various levels of production and remains constant at all levels of output include rent, insurance, interest, depreciation etc. Second is the variable cost. It depends upon the amount of output and varies with it that is it keeps on varying levels of production vary and include material cost, labor cost, advertising expenses etc. The fixed cost is independent of X. Variable cost is directly proportional to X. Here C is the cost curve and this portion of the total cost represents the fixed cost. So we can say that total cost is equal to fixed cost plus variable cost that is total cost C is equal to fixed cost F plus variable cost V and the cost function that is C is equal to C of X which can be written as F plus V of X. The graph of the cost function C is equal to C of X is called the cost curve and the fixed cost is determined by the intersection of the cost curve with the cost axis that is the value of C when X is equal to 0. Let us take an example if the cost function is given by C of X is equal to 2 into X raised to power 4 plus 5 by 3 into X raised to power 3 plus X plus twice of E plus 5. Then here the fixed cost is given by C of 0 that is we put the value of X of 0 in C of X and we get twice of E and variable cost is given by 2 X raised to power 4 plus 5 by 3 into X raised to power 3 plus X. Now we are going to discuss demand function. Demand function is said to represent the functional relationship between demand and price of a commodity. The demand for a product is considered to be dependent on its price only though it depends upon the number of factors such as taste of the consumer, quality, price, disposable income, wealth etc. But all the factors other than the price are taken as constant to facilitate the study of the demand function. If the number of units demanded by a consumer is P per unit then demand function is written explicitly as is equal to F of P in implicit format is equal to 0 in demand function is equal to F of P that is X is the dependent variable, the value of X is greater than equal to 0 is the independent variable, the value of P is greater than equal to 0 as demand and price cannot be negative. Now as price increases demand decreases and as price decreases demand increases hence the demand curve is a decreasing curve. Next we have revenue function. Let us define revenue first. Revenue can be defined as the amount of money received from the sales of goods. It depends upon the selling price of the product and the actual quantity sold. Therefore total revenue is equal to quantity sold into selling price per unit of the commodity since the total revenue P is equal to F of X the only demand function where P is price per unit of a certain commodity when X units are sold. Therefore the total revenue R is given by R of X is equal to P into X. Now the demand function is equal to F of X. Therefore the total revenue function R of X becomes X into F of X. Now we are going to discuss profit function as profit is the difference of the total revenue and total cost that is profit is equal to total revenue minus total cost. Therefore profit function that is P of X can be expressed as P of X is equal to R of X minus of C of X where P of X is the total profit where R of X is the total revenue received on selling X units of the commodity Now C of X is the total cost on producing and marketing X units of the commodity. Now we shall discuss the basic point. It is a point of no profit, no loss accompaniment begins to earn a profit. We can say that it is that point where total revenue equals total cost we know that profit that is P of X is equal to total revenue that is R of X minus total cost that is C of X for the value of X greater than zero The given point is equal to zero which implies that R of X is equal to C of X the value of X obtained on solving this equation determines the break even point. Graphically break even point is the point of intersection of the revenue curve and the cost curve Before the break even point or company faces loss at the break even point or company begins to earn a profit. Therefore this area is called loss area and the area after the break even point is called the profit area. The general equation for finding break even point is S is equal to S C plus V C where S denotes S, S C is the fixed cost and V C is the variable cost The variable cost V C, fixed cost F C and S S are used for finding company's break even point detailed question that you enjoyed this question.