(Cost - Revenue) Function Report

Report: (Cost – Revenue) Function
Team Members:
DR. Ahmed Khalifa

Table of Contents
1.............................................................................................................Abstract:3
2...............................................................................................Problem Statement4
3............................................................................Proposed Solution Methodology4
A. Develop a 2D plot for demand versus the price:..........................................................................4
B. Develop a 2D plot for average cost versus the quantity:..............................................................5
C. Compute the demand elasticity when price equal to 1:................................................................6
D. Compute the marginal cost when the quantity is equal 1:............................................................7
E. Develop the profit function:........................................................................................................7
F. Find the quantity that maximizes the total profit:........................................................................8
G. What is the price that maximizes the profit?................................................................................8
H. What is the maximum profit?......................................................................................................8
4................................................................................................MATLAB Output9
5....................................................................................Conclusions and Summary10
2

Abstract:
This project considers a managerial task of analyzing the cost function, the revenue
function and the profit function of the company. The revenue function will be derived from the
demand function; the extrema analysis is performed. The latter includes the location of the
maximum of the profit with the help of the first derivative and refining this with the help of the
second derivative. Additionally, the graphical representation of the revenue, profit and average
cost function is given.
3

Problem Statement
The aim of this project was to solve a business problem mathematically in a way that it
can be presented to a manager for decision making purposes. MATLAB was used as the tool of
analysis. The manager is specifically presented with the following total cost function;
C(q)=0.8q2+25q+6000
The management has such a function for the cost and it is true for the production of q
units.
From the given total cost function, we can derive the average cost function as follows;
́C(q)=C(q)
q=0.8q2+25q+6000
q
¿0.8q+25+6000
q
Proposed Solution Methodology
A. Develop a 2D plot for demand versus the price:
The first part of this report sought to develop a 2D plot for the demand versus the price.
The MATLAB code used is given below;
>> p=linspace(0,50,500);
>> q=10000-95*p;
>> plot(p,q)
4