MATH BLOG

Greeting Students;

In today's lecture we will be discussing Math Concept of “Profit, Revenue function” which is up and running under our Blog Board link, this class latest participation date is Apr 20^th, 2015 @ 11:59 PM. No participation(s) will be accepted after this due date. Feel free to ask questions if you have any.

Prof. Malk AlHarbi

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Profit, Revenue function

The profit- revenue function is a function that shows the gains made by a company in production in a mathematical form.

It is equivalent to: Total revenue (TR) – (TC)

Total revenue = P * Q

It is the total amount of income gained from selling the finished products of a production process.

Total cost =Fixed cost + Variable cost( Cost per unit * Quantity)

Profit revenue function = TR –TC

At maximum profit, the slope of the profit function (Marginal profit) = 0

ddQ  = dTR/ dQ – dTC / dQ = 0

dTR/ dQ = dTC/ dQ

But dTR / dQ = MR

And

dTC/ dQ = MC

Thus MR = MC for profit maximization.

This is the necessary condition for profit maximization. 

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Example

Consider a company that has:

·         fixed costs of $12000 and variable costs of  100 * q  if the cost of producing one unit is $100, thus total costs = Fixed costs + variable costs i.e.  $12000 + 100q

·         Total revenue of 180 *q if one unit is sold for $180

The profit revenue function = TR – TC

180q – (12000 + 100q)

= 80q – 12000

Next, we find the Break- even value which

 Occurs when total revenue = total cost

Thus; 180q = 12000 + 100q

80q = 12000

Q = 150

The revenue = p* q

 = 180 * 150

= 27000

Thus break even value = $27000

We can then plot a graph showing the break- even point, revenue and the cost functions.

If 100 is the number of items produced, we come up with the following graphical representation.

The break- even point on the graph is a point where the total revenue = total cost (TR = TC)

The profit – revenue graph will be as follows:

For profit maximization, we differentiate with respect to Q

Thus 80Q – 12000 = 0

dMR/dQ = 80

Thus profit is maximized at 80 units.

Profit = 80 *80 – 12000

= 16000 – 12000

= $4000