Business Decision Analysis - Case Study

Business Decision Analysis
Case Study
Student Name
[Pick the date]

PURPOSE OF THE REPORT
The main objective of this report is to provide advice to the company in relation to the optimum
number of basketballs and footballs that need to be produced so as to maximise the net profit
after tax for the company. In this regards, the requisite model has been framed for the given
problem which had been described in the following section. The model has been solved using
MS-Excel in order to provide optimum production units for profit maximisation.
DESCRIPTION OF THE PROBLEM
The given problem relates to a sports manufacturer named ABCD Ltd and has multiple
manufacturing plants. A particular plant of the company is dedicated for production of
basketballs and footballs. The company has some flexibility with regards to the production of
footballs and basketballs and hence can alter the production level of these products. These
various costs related to the production of these products on a per unit basis has been provided.
Additionally, the unit selling price for each of the items is known. Further, there are certain
constraints at the manufacturing plant with regards to machine hours available and also the
minimum and maximum production of each product. Considering these constraints, it is
imperative to determine the ideal product mix for the two products which would lead to
maximum profit generation for the company.
METHODOLOGY
In order to resolve the problem at hand, the given problem would be formulated as a linear
programming problem and then solved using Excel function SOLVER considering the key inputs
and resource & production constraints.
Formulation of Linear Programming Model
The given information and data are summarized below.
Minimum Maximum
Total available machine hours 39,000 40,000
Number of basketballs that can be
manufactured
30,000 60,000
1

Number of footballs that can be
manufactured
20,000 40,000
Basketballs Footballs
Time to manufacture balls (hours) 0.5 0.3
Cost of labour (1 machine hour ) ($) 6 6
Cost of material ($) 2 1.25
Basketballs Footballs
Selling price per piece ($) 14 11
Corporate tax rate 28%
The aim is to maximize the net profit of ABCD Ltd by determining the idea number of footballs
and basketballs that needs to be manufactured.
Profit per unit
For basketball = Selling price – (Labour cost + material cost) ¿ 14−{(0.5∗6)+2}=$ 9
For football = Selling price – (Labour cost + material cost) ¿ 11−{(0.3∗6)+1.25 }=$ 7.95
Let the decision variables are x and y and profit z.
x=Number of basketballs
y=Number of footballs
Objective function
Max profit ( z ) =9 x +7.95 y ... ... ... ... ... ... .. ( before tax )
2