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Functions: Cost, Revenue, and Profit










































A biscuit factory has the following fixed and variable manufacturing costs:

- daily fixed costs of RM500.

- costs 80 cents to produce each bag of biscuits.


In addition, the revenue per unit sold is:

- A bag of biscuits sells for RM 1.80.


Given that x represents the number of bags of biscuits sold,

(a) Find

(i) Cost function, C(x)
C(x) =

(ii) Revenue function, R(x)

(iii) Profit function, P(x)


(b) Calculate the daily profit if the factory sells 1200 bags of biscuits daily.

Comments for Functions: Cost, Revenue, and Profit

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Jul 24, 2012
Functions - Cost, Revenue, and Profit
by: Staff


The answer:


RM = Ringgit Malaysia

(MYR = currency code)



(a)(i) Cost function, C(x)


Linear Manufacturing Cost Function = Fixed Cost + (Average Variable Cost) * Output

C(x) = Fixed Cost + (Average Variable Cost) * Output


DAILY fixed costs = RM500

C(x) = RM500 + (Average Variable Cost) * Output


VARIABLE costs: 80 cents to produce each bag of biscuits

C(x) = RM500 + (80 cents) * Output


x represents the number of bags of biscuits sold (we will assume the number of bags sold is equal to the number of bags manufactured)

C(x) = RM500 + (80 cents) * x


>>> Daily Cost Function: C(x) = 500 + (.80) * x



---------------------------------------------

NOTE - For your information:

A linear production function [such as C(x) = 500 + (.80) * x] is strictly a short term forecasting tool. It does not take into account the Law of Diminishing Returns.

To take the Law of Diminishing Returns into account, you can use:

- the quadratic production function:

or

- the cubic production function

or

- the power function

---------------------------------------------



(a)(ii) Revenue function, R(x)

The DAILY revenue is the selling price of a bag of biscuits multiplied by the number of bags sold that day.

R(x) = (Selling Price) * (bags sold)

A bag of biscuits sells for RM 1.80

R(x) = (1.80) * (bags sold)

(we will again assume the number of bags sold is equal to the number of bags manufactured)

R(x) = (1.80) * x

>>> Revenue Function: R(x) = (1.80) * x


(a)(iii) Profit function, P(x)

The profit is the difference between revenue received and cost of manufacturing.

P(x) = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = (1.80) * x - [500 + (.80) * x]

P(x) = [(1.80) * x - (.80) * x] - 500

P(x) = [(1.80 - .80) * x] - 500

P(x) = [(1.00) * x] - 500

P(x) = (1.00)x - 500

P(x) = x – 500


>>> Daily Profit Function: P(x) = x - 500



(b) Calculate the daily profit if the factory sells 1200 bags of biscuits daily.

Daily Profit Function: P(x) = x - 500

P(x) = x - 500

P(x) = 1200 - 500

P(x) = 700


>>> Daily Profit: P(x) = RM 700




Thanks for writing.

Staff
www.solving-math-problems.com



Feb 07, 2021
l NEW
by: Anonymous

Consider a manufacturing process that produces 5000 units at a cost of $600,000 and 10,000 units at a cost of $800,000. Each unit produced can be sold for $100. Assume a linear relationship exists between the number of units produced and cost.
Find the average cost per unit of producing 50,000 units.

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