Optimal Jacket Manufacturing for Maximum Profit

The assignment is about formulating a linear programming model to determine the optimal mix of three types of Dotti jackets (Denim, Bomber, and Biker) that should be manufactured to maximize the profit margin. The manufacturing costs and time required for each process step are given, as well as the total monthly hours available. The goal is to allocate resources efficiently to maximize profits, with Denim jackets having the highest contribution margin per unit input, followed by Bomber jackets.

Sustainable Accounting and Strategic Management
Linear Programming Problem
Student Id
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Question 3
1. Linear Programming Problem
Give data and information has been summarized below.
 The manufacturing costs related to the three types of Dotti jackets are given below:
 It has been given that all three types of jackets go through the same type of manufacturing
processes. The time required for each process step and the total monthly hours available are
highlighted below:
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Formulation of linear programming model
 Aim
The aim is to formulate the linear programming model to determine the optimal mix of the
jackets that should be manufactured to maximize the profit margin.
 Table to show the profit margin of each of the jackets is shown below:
 Assumption
Let x=Unit produced of biker jackets
y=Unit produced of bomber jackets
z=Unit produced of Denim jackets
 Model
Objective function
Max P=18 x+ 15.27 y+12.25 z
Subject to constraints
0.3 x+0.25 y+0.2 z ≤1100
0.15 x+0.15 y+ 0.1 z ≤600
0.35 x+0.35 y+ 0.25 z ≤1500
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0.1 x+ 0.1 y +0.1 z ≤ 500
x , y , z ≥ 0(Non−negativity constraints)
 Output from excel solver
 Answer report
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 Sensivity report
The optimal values and the optimum solution are highlighted below:
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x=Unit produced of biker jackets=0
y=Unit produced of bomber jackets=2000
z=Unit produced of Denim jackets=3000
Max P=$ 67,290
2. It is apparent from the solver analysis that highest contribution margin per unit input is for
Denim jackets. Further, the next highest contribution margin per unit input is observed for
Bomber jackets and last in the list is Biker jacket. As a result, it makes sense that the maximum
resources must be allocated to the Denim jackets only which is confirmed by the solver output
also. Further, except stitching all the other resources are constraints as at the current production
level, the monthly hours are being completely utilized. Hence, in order to enhance profits, more
resources should be made available Also, the focus of the production should be limited to only
Denim and Bomber varieties of jackets.
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