The Problem: Merton Truck Company has been experiencing difficulties related to their financial performance, and they do not know which is the optimal product mix to maximize profits and performance. Group 2 was asked to make recommendations and analyze the given situation to eliminate the difficulties and come up with the right product mix and the optimal solutions considering different alternatives and scenarios.
The Solution: Linear Programming was used to analyze the different alternatives to arrive at the optimal solution. The optimal product mix was calculated to be 2000 units of model 101 and 1000 units of model 102. In the next pages you will see the answers ...view middle of the document...
A third variable in respect of the proposed model 103 truck is introduced later.
The problem has four constraints. They reflect limitations imposed by capacity in the engine assembly line, metal stamping line, model 101 assembly line and model 102 production line.
The objective aim of the analysis is to maximize contribution/profits. The objective function calculates the profits by determining the optimal units of each truck to be produced and multiplying same with its contribution margin.
In this section, we are calculating the optimal product mix under different scenarios.
Fixed costs will not be affected by the mix of products so it shall be deducted after we calculate the total profit
if we disregard the fixed over head we shall have the following costs (include only variable overhead):
Per unit Model 101 Model 102
Direct Material 24000 20000
Direct Labor 4000 4500
Variable overhead 8000 8500
Cost: 36000 33000
Subtract from Selling Price
Selling Price 39000 38000
Cost 36000 33000
Profit (without FO) 3000 5000
Using Excel Solver we can calculate the Total production units of models 101 and 102, and the
Model 101 102
Profit per unit 3000 5000
Production 2000 1000 Total
Profit 6000000 5000000 11000000
constraints Model 101 Model 102 usage RHS Leftover
Engine Assembly 1 2 4000 TRUE 4000 0
Metal stamping 2 2 6000 TRUE 6000 0
Model 101 assembly 2 0 4000 TRUE 5000 1000
Model 102 assembly 0 3 3000 TRUE 4500 1500
However now we need to deduct the fixed overhead costs which are $8.6 million from the $11.00 million. Maximum profit after deducting the fixed overhead costs is $2.4 million
When there are potential changes in the parameter of LP models, Sensitivity Analysis is required. Here we have an increase in the RHS value of the Engine assembly constraint from 4000 to 4001. Each extra unit of capacity of Engine Assembly is worth $2000 (shadow price of engine assembly capacity) because all the hours were used up.
The contribution per unit or the objective coefficient for model 102 is 5000 $ so to maximize the profit we should produce one more unit of model 102
Each extra unit of capacity of engine assembly is worth $2000 (shadow price of engine assembly capacity).
100 extra units of capacity of engine will be worth $ 200,000 which is 100 times the value of one extra unit of capacity ($2000)
The allowable increase is 500 units so it is safe to say that a change might occur in the value of any additional unit in the capacity only if we exceed that limit. See appendix A for more details
Under this question Merton Trucks management is considering the option of outsourcing engine assembly in order to maximize returns.
In order to relieve the capacity problem in the engine...