Revenue, cost and profit by shas production 2014

2014

Shas

Production

[ Cost, Revenue and Profit Models] To mathematically model a situation means to represent it in mathematical terms. The particular representation used is called a mathematical model of the situation.

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Cost, Revenue and Profit

Models: -

Take a look at the third example above, where

the total cost of purchasing a number of items

(sodas) was expressed as a function of the

number of items x. This function is an example

of a cost function. The rest of this explanation

will appear here only after you correctly entered

the function in the third example above.

Cost Function

A cost function specifies the cost C as a

function of the number of items x. Thus, C(x) is

the cost of x items, and has the form

Cost = Variable cost + Fixed cost

Where the variable cost is a function of x and

the fixed cost is a constant. A cost function of

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the form

C(x) = mx + b

Is called a linear cost function; the variable cost

is mx and the fixed cost is b. The slope m,

the marginal cost, measures the incremental

cost per item.

Example

The daily cost to your company to

print x paperback sci-fi novels is

C(x) = 3.50x + 1200 dollars.

Note that C is measured in dollars, and x is

measured in books (paperback sci-fi novels, to

be precise).

The marginal cost is m = 3.5, and the fixed cost

is b = 1200.

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The daily cost if you print no books is

$

The daily cost to print 100 books is $

The daily cost to print 101 books is $

The daily cost to print

each additional book is $

The variable cost is $

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Revenue Function

The revenue resulting from one or more

business transactions is the total payment

received, sometimes called the gross proceeds.

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If R(x) is the revenue from selling x items at a

price of m each, then R is the linear

function R(x) = mx and the selling price m can

also be called the marginal revenue.

Example

Suppose that your publishing company sells sci-

fi paperbacks to a large retailer for $6.50 per

book. Then

R(x) = 6.50x dollars.

The marginal revenue is m = $6.50 per book.

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Profit Function

The profit is the net proceeds, or what remains

of the revenue when costs are subtracted. If

the profit depends linearly on the number of

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items, the slope m is called the marginal

profit. Profit, revenue, and cost are related by

the following formula.

Profit = Revenue − Cost

P = R − C

If the profit is negative, say −$500, we refer to

a loss (of $500 in this case). To break

even means to make neither a profit nor a loss.

Thus, break even occurs when P = 0, or

R = C

Break Even

The break-even point is the number of

items x at which break even occurs.

Example

Going back to the sci-fi novels, we already have

the cost and revenue functions:

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C(x) = 3.50x + 1

200 dollars. Daily cost to make x books

R(x) = 6.50x dol

lars.

Revenue from the sale

of x books

The profit function

is P(x) = dollars

For break-even, x = books

The marginal profit is dollars/item

Thus, you should sell??? Books per day to break

even, and more than that to make a profit of

$??? Per additional book. ($??? is the marginal

profit.)

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Revenue, cost and profit by shas production 2014

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