  # 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

 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.