BUS107e Assignment: Linear Programming and Forecasting Analysis

This project delves into the application of linear programming and forecasting techniques through two case studies. The first case study focuses on optimizing a loan plan for Mathew, considering factors like sales revenue, bills, and interest rates. The analysis explores the impact of varying interest rates and changes in bill payments and sales forecasts on the optimal loan structure. The second case study applies forecasting methods to predict monthly paid lettings for a China-based boutique. The project compares different forecasting methods, including multiplicative moving average, exponential, and regression methods, using MAD and MAPE to determine the most accurate method. It then uses the exponential method to forecast paid lettings for the year 2019. Additionally, the project analyzes the standard error (SE) to determine the relevant time periods for forecasting and discusses the limitations of the exponential forecasting method. This project is a valuable resource for students studying quantitative methods and business development, offering practical examples and solutions for real-world problems.

Running head: LINEAR PROGRAMMING AND FORECASTING
Linear Programming and Forecasting
Name of the Student:
Name of the University:
Author’s Note:

1LINEAR PROGRAMMING AND FORECASTING
Table of Contents
Introduction:....................................................................................................................................2
Answer 1.A:.....................................................................................................................................2
Answer 1.B.1...................................................................................................................................4
Answer 1.B.2...................................................................................................................................5
Answer 1.B.3...................................................................................................................................7
Answer 3.A......................................................................................................................................8
Answer 3.B......................................................................................................................................9
Conclusion.....................................................................................................................................10
Reference:......................................................................................................................................11

2LINEAR PROGRAMMING AND FORECASTING
Introduction:
Linear programming is extensively utilized in mathematical modelling and techniques
which is applied to obtain the most favourable results or solutions with respect to the given
various constraint that are expressed in a linear relationship (Dantzig, 2016). Forecasting is
important to make plans for effective operations. Planning is not possible without prediction of
future and forecasting is an analysis of the future (De Giorgi, Congedo, & Malvoni, 2014).
Here two case studies are where linear programming and forecasting is widely applied.
The linear programming model have to derive the optimum loan plan that minimises the total
amount of loan interest for Mathew and the forecast of monthly paid lettings needs to be done for
China-based boutique. The results of these two case studies are discussed below (Vanderbei,
2015).
Answer 1.A:
Table 1: Optimum Loan Plan for Mathew
Month Sales Revenue ($) Bills ($) LHS RHS
January $ 4,000.00 $ 6,000.00 $ - $ -
February $ 3,000.00 $ 5,000.00 $ 0.00 $ -
March $ 3,000.00 $ 4,000.00 $ -0.00 $ -
April $ 3,000.00 $ 3,000.00 $ - $ -
May $ 5,000.00 $ 4,000.00 $ -0.00 $ -
June $ 9,000.00 $ 1,000.00 $ 5,283.83 $ 5,283.83
July $ 3,000.00 $ 6,000.00 $ 2,283.83 $ 2,283.83
August $ 2,000.00 $ 6,000.00 $ - $ -

3LINEAR PROGRAMMING AND FORECASTING
September $ 1,000.00 $ 4,000.00 $ 0.00 $ -
October $ 2,000.00 $ 2,000.00 $ - $ -
November $ 6,000.00 $ 1,000.00 $ -0.00 $ -
December $ 10,000.00 $ 1,000.00 $ 8,000.00 $ 8,000.00
The required loan structure derive from the above calculation is as follows:
Value
L 1596.387
S1 403.6133
S2 2413.704
S3 3474.046
S4 3560.897
S5 2649.92
S6 0
S7 0
S8 1716.168
S9 4759.072
S10 4878.049
S11 0
S12 787.9531

4LINEAR PROGRAMMING AND FORECASTING
The total amount of loan is 26239.809 out of which annual loan is 1596.387 and the rest
of the loan amount is distributed in months from January to December with the assumption that
Mathew has zero balance in the beginning of the year.
Answer 1.B.1
Table 2: The Optimum Loan Plan for the Interest Rate of 10.5%
Month Sales Revenue ($) Bills ($) LHS RHS
January $ 4,000.00 $ 6,000.00 $ - $ -
February $ 3,000.00 $ 5,000.00 $ - $ -
March $ 3,000.00 $ 4,000.00 $ - $ -
April $ 3,000.00 $ 3,000.00 $ - $ -
May $ 5,000.00 $ 4,000.00 $ - $ -
June $ 9,000.00 $ 1,000.00 $ 5,283.83 $ 5,283.83
July $ 3,000.00 $ 6,000.00 $ 2,283.83 $ 2,283.83
August $ 2,000.00 $ 6,000.00 $ - $ -
September $ 1,000.00 $ 4,000.00 $ - $ -
October $ 2,000.00 $ 2,000.00 $ - $ -
November $ 6,000.00 $ 1,000.00 $ - $ -
December $ 10,000.00 $ 1,000.00 $ 8,000.00 $ 8,000.00
The required loan structure derive from the above calculation is as follows:
Value
L 1596.387

5LINEAR PROGRAMMING AND FORECASTING
S1 403.6133
S2 2413.704
S3 3474.046
S4 3560.897
S5 2649.92
S6 0
S7 0
S8 1716.168
S9 4759.072
S10 4878.049
S11 0
S12 764.0073
From the above loan structure, it is observed that the initial loan structure for
question 1.A has not changed due to the fall in the interest rate on annual loan from 12% to
10.5%. Hence it can be said that there is no impact of the change in rate of interest on the optimal
loan plan.
Sensitivity Report

6LINEAR PROGRAMMING AND FORECASTING

7LINEAR PROGRAMMING AND FORECASTING

8LINEAR PROGRAMMING AND FORECASTING
Answer 1.B.2
Table 3: Loan Plan When the Bill to Pay of October is $3500
Month Sales Revenue ($) Bills ($) LHS RHS
January $ 4,000.00 $ 6,000.00 $ 879.74 $ 879.74
February $ 3,000.00 $ 5,000.00 $ - $ -
March $ 3,000.00 $ 4,000.00 $ -0.00 $ -
April $ 3,000.00 $ 3,000.00 $ - $ -
May $ 5,000.00 $ 4,000.00 $ -0.00 $ -
June $ 9,000.00 $ 1,000.00 $ 6,711.55 $ 6,711.55
July $ 3,000.00 $ 6,000.00 $ 3,711.55 $ 3,711.55
August $ 2,000.00 $ 6,000.00 $ - $ -
September $ 1,000.00 $ 4,000.00 $ 0.00 $ -
October $ 2,000.00 $ 3,500.00 $ 0.00 $ -
November $ 6,000.00 $ 1,000.00 $ -0.00 $ -
December $ 10,000.00 $ 1,000.00 $ 8,000.00 $ 8,000.00
The required loan structure derive from the above calculation is as follows:
Value
L 2879.742
S1 0
S2 1120.258
S3 2148.265

9LINEAR PROGRAMMING AND FORECASTING
S4 2201.971
S5 1257.021
S6 0
S7 0
S8 288.4462
S9 3295.657
S10 4878.049
S11 0
S12 2225.311
From the above loan structure it is observed that the initial loan structure for question 1.A
has changed due to the change in bill payment of October. Hence it can be said that due to
increase in the bill payment in October from 2000 to 3500, both the amount of annual loan and
monthly needs to be increased to achieve the targeted cash flow in the end of the year.
Sensitivity Report

10LINEAR PROGRAMMING AND FORECASTING

11LINEAR PROGRAMMING AND FORECASTING