Merton Truck Company case analysis

1. Section 1 ; Group 2
FT 12113 Anuja Dash
FT 12102 Abhay Bohra
FT 12189 Pramod Ravi Shankar
FT 12127 Harendra Singh
FT 12168 Tushar Arora
FT 12104 Abhilash Mohapatra

2. Specification Model 101 Model 102
DM 24000 20000
Direct Labour
Engine assembly 1200 2400
Metal Stamping 800 600
Final Assembly 2000 1500
Total DL 4000 4500
Variable Overhead
Engine assembly 2100 4000
Metal Stamping 2400 2000
Final Assembly 3500 2500
Total Variable Overhead 8000 8500
Selling Prices 39000 38000
Total Variable Cost 36000 33000
Contribution Margin per Unit 3000 5000
Section 1: Group 2: PAAATH 4/8/2012 2

3. Fixed Overhead
Engine assembly 1700000
Metal Stamping 2700000
Final Assembly 2700000 1500000
Total Fixed Over Head 8600000
Section 1: Group 2: PAAATH 4/8/2012 3

4. Engine Assembly 1* Model 101 2* Model 102 <= 4000
Metal Stamping 2* Model 101 2* Model 102 <= 6000
Model 101 assembly 2* Model 101 0* Model 102 <= 5000
Model 102 assembly 0* Model 101 3* Model 102 <= 4500
Non Negative Model 101 1* Model 101 0* Model 102 >= 0
Non Negative Model 102 0* Model 101 1* Model 102 >= 0
Maximize Profit = UCM Model 101*units Model 101+ UCM Model
102*units Model 102 -Fixed Overheads
Section 1: Group 2: PAAATH 4/8/2012 4

5. Variables
Model 101 Model 102 Objective
2000 1000 2400000
Section 1: Group 2: PAAATH 4/8/2012 5

6. Sensitivity Analysis
Final Reduced Objective Allowable Allowable
Name Value Cost Coefficient Increase Decrease
Model 101 2000 0 3000 2000 500
Model 102 1000 0 5000 1000 2000
Final Shadow Constraint Allowable Allowable
Name Value Price R.H. Side Increase Decrease
Engine Assembly 4000 2000 4000 500 500
Metal Stamping 6000 500 6000 500 1000
Model 101 assembly 4000 0 5000 1E+30 1000
Model 102 assembly 3000 0 4500 1E+30 1500
Non Negative Model 101 2000 0 0 2000 1E+30
Non Negative Model 102 1000 0 0 1000 1E+30
Section 1: Group 2: PAAATH 4/8/2012 6

7. Shadow price of Engine Assembly is 2000 $
So if Assembly unit capacity is increased from 4000 to 4001 then
Extra unit Engine Assembly capacity is worth 2000$
Variables
Model 101 Model 102 Objective
1999 1001 2402000
Section 1: Group 2: PAAATH 4/8/2012 7

8. If capacity of Engine Assembly is increased to 4100
Increase in profit due to 100 unit increase in production capacity
=2600000-2400000
=200000
Variables
Model 101 Model 102 Objective
1900 1100 2600000
Section 1: Group 2: PAAATH 4/8/2012 8

9. 500 Units of Engine Assembly capacity can be added before it capacity
worth changes.
Profit at 4500 & 4501 is same i.e. production decision does not change
Objective
3400000
Variables
Model 101 Model 102
1500 1500
Section 1: Group 2: PAAATH 4/8/2012 9

10. Max We can have 500 Hr increase in capacity and profit Contribution
Increase 2000$ per hr
So max we can pay that much
Variables
Model 101 Model 102 Objective
1500 1500 3400000
Section 1: Group 2: PAAATH 4/8/2012 10

11. Constraints
Engine Assembly 1 2 0.8 4000 <= 4000
Metal Stamping 2 2 1.5 6000 <= 6000
Model 101 assembly 2 0 1 4000 <= 5000
Model 102 assembly 0 3 0 3000 <= 4500
Non Negative Model 101 1 0 0 2000 >= 0
Non Negative Model 102 0 1 0 1000 >= 0
Non Negative Model 103 0 0 1 0 >= 0
Profit= UCM Model 101*units Model 101+ UCM Model 102*units
Model 102+ UCM Model 103*units Model 103 - Fixed overheads
Section 1: Group 2: PAAATH 4/8/2012 11

12. We should not produce Model103
Variables
Model 101 Model 102 Model103 Objective
2000 1000 0 2400000
Section 1: Group 2: PAAATH 4/8/2012 12

13. Final Reduced Objective Allowable Allowable
Name Value Cost Coefficient Increase Decrease
Model 101 2000 0 3000 2000 500
Model 102 1000 0 5000 1000 2000
Model103 0 0 2000 350 1E+30
Final Shadow Constraint Allowable Allowable
Name Value Price R.H. Side Increase Decrease
Engine Assembly 4000 2000 4000 500 500
Metal Stamping 6000 500 6000 500 1000
Model 101 assembly 4000 0 5000 1E+30 1000
Model 102 assembly 3000 0 4500 1E+30 1500
Non Negative Model 101 2000 0 0 2000 1E+30
Non Negative Model 102 1000 0 0 1000 1E+30
Non Negative Model 103 0 -350 0 2857.142857 0
Section 1: Group 2: PAAATH 4/8/2012 13

14. Model 103 CM should be more than > 2350 in order to make it worthy
of production
With 2351 CM for Model 103 we get the following production schedule
Variables
Model 101 Model 102 Model103 Objective
0 857.14286 2857.1429 2402857
Section 1: Group 2: PAAATH 4/8/2012 14

15. Clearly from sensitivity analysis 500 Units of Engine Assembly capacity can be
added. More than that will make no improvement
Variables
Model 101 Model 102 Objective
2000 1000 2400000
Section 1: Group 2: PAAATH 4/8/2012 15

16. Constraints
Engine Assembly 1 2 4500 <= 6000
Metal Stamping 2 2 6000 <= 6000
Model 101 assembly 2 0 3000 <= 5000
Model 102 assembly 0 3 4500 <= 4500
Non Negative Model 101 1 0 1500 >= 0
Non Negative Model 102 0 1 1500 >= 0
Section 1: Group 2: PAAATH 4/8/2012 16

17. So Additional revenue =-50000$
Variables
Model 101 Model 102 Objective
1500 1500 3400000
New Contribution 3400000
Increase in fixed cost 750000
Increase in labour 250*3600$ 900000
labour Cost saving 500*1200$ 600000
Net Contribution 2350000
Section 1: Group 2: PAAATH 4/8/2012 17

18. We have to add new constraint of product mix
Constraints
Engine Assembly 1 2 <= 4000
Metal Stamping 2 2 <= 6000
Model 101 assembly 2 0 <= 5000
Model 102 assembly 0 3 <= 4500
Non Negative Model 101 1 0 >= 0
Non Negative Model 102 0 1 >= 0
Product ratio Constraint -1 3 = 0
Section 1: Group 2: PAAATH 4/8/2012 18

19. Additional Contribution Due to this decision is =2400000$ - 1900000$
=500000$
Variables
Model 101 Model 102 Objective
2250 750 1900000
Section 1: Group 2: PAAATH 4/8/2012 19

20. Section 1: Group 2: PAAATH 4/8/2012 20