An Introduction To Business Decision Modelling

Chen Zhimin(陈智民 )

School of Management

Shenzhen University

Office: 文科楼 2403

Tel: 26534104(O) 13902972552(Mobile)

Email: chenzm@szu.edu.cn

1. The Structure of Linear Models

The general expression for a straight line:

y=a+bx y and x: dependent /independent variables of int

erest a and b: constants, coefficients, parameters

a: Intercept--- y=a+b(0)=ab: Slope (Gradient)

b=the change in y/unit change in x

=y/ x

Example: y=3+2x Intercept: a=3 Slope: b=y/ x=2

Shifts of a straight line Changes in the intercept

y=7+2xy=-2+2x

Changes in the slopey=3+5xy=3+1x

Two fundamental types of shifts of straight line: Parallel shift: changes in the intercept Pivotal shift: changes in the slope

Break Even Analysis

A company/firm: Make a single product Capacity: 150 Price: 20 Fixed cost: 500 Variable cost: 15 Find Break-Even Point

Production Potential 0-150 units

Revenue Consideration Total Revenue(TR)

TR=pq p ----selling price/unit q ----quantity sold Example: TR=0+20q (comparison with y=a+bx)

Average Revenue(AR)AR=TR/q=pq/q=p

Marginal Revenue(MR)MR=(the changes in TR)/(a unit changes in q)=

= TR/ q

Cost Considerations Fixed Cost(FC)

Irrespective of how many units of output are produced: annual rental charges, management cost,..

Total Variable Cost(TVC)TVC=VCqVC: variable cost per unit: labour/material paym

ent

Total Cost(TC) TC=Fixed Cost +Total Variable Cost

=FC+VCq Example: TC=500+15q

(compared with y=a+bx)

Average Cost(AV) AV=TC/q

Marginal Cost(MC) MC= TC/ q

Break Even Analysis Diagram 1.4 System of linear equations:

TR=0+20q

TC=500+15q

TR=TC (Break Even)

Break Even SolutionTo scan Table 1.2To read Diagram 1.4To solve the system of linear simultaneous

equations

The rule to write the system of linear equations:

The unknowns have been written in a specific , consistent order in each equation

All terms involving unknowns have been taken to the Left Hand Side (LHS) of each equation

All constants are taken to the Right Hand Side (RHS) of each equation

The coefficients of each unknown are carefully identified in each equations, including 0 and 1

1TR+0TC-20q=00TR+1TC-15q=5001TR-1TC- 0q=0