Question

Given the following table, describing a process with a current output of 2500 units, complete the static and dynamic analysis; determine the trade-off point, plot the two system’s costs curves, and describe which system would be the most cost effect at the current output, 5000 units of output and 8000 units of output

System 1 System 2

Packaging $150.00 $95.00

Storing & Handing $125.00 $75.00

Inventory carrying $200.00 $25.00

Transportation $105.00 $150.00

Administrative $45.00 $30.00

Fixed Plant & Equipment $1,750.00 $2,250.00

Total Cost $2,375.00 $2,625.00

Answer 1

1. Calculation of Cost for each System:

System 1	2500	5000	8000
Packaging	150.00	300.00	480.00
Storing & Handing	125.00	250.00	400.00
Inventory carrying	200.00	400.00	640.00
Transportation	105.00	210.00	336.00
Administrative	45.00	45.00	45.00
Fixed Plant & Equipment	1,750.00	1,750.00	1,750.00
Total Cost	2,375.00	2,955.00	3,651.00

System 2	2500	5000	8000
Packaging	95.00	190.00	304.00
Storing & Handing	75.00	150.00	240.00
Inventory carrying	25.00	50.00	80.00
Transportation	150.00	300.00	480.00
Administrative	30.00	30.00	30.00
Fixed Plant & Equipment	2,250.00	2,250.00	2,250.00
Total Cost	2,625.00	2,970.00	3,384.00

The Most Cost Effect of the above two systems at : 1. 5000 units - System 1 2. 8000 units - System 2

2. The Cost Curves of the 2 systems are as follows :

Total Cost	2500 units	5000 units	8000 units
System 1	2,375.00	2,955.00	3,651.00
System 2	2,625.00	2,970.00	3,384.00

3. The Trade off Point is the Point at which the Cost is equal for both the systems

Therefore if the trade point is X, then at System 1 & System 2, Total Cost = X * Variable Cost + Fixed Cost

Breakup of Fixed and variable cost under each system is as follows :

System 1	At 2500 Units	Cost per Unit
Variable Cost
Packaging	150.00	0.06
Storing & Handing	125.00	0.05
Inventory carrying	200.00	0.08
Transportation	105.00	0.04
TOTAL		0.23
Fixed Costs
Administrative	45.00
Fixed Plant & Equipment	1,750.00
TOTAL	1,795.00

System 2	At 2500 Units	Cost per Unit
Variable Cost
Packaging	95.00	0.04
Storing & Handing	75.00	0.03
Inventory carrying	25.00	0.01
Transportation	150.00	0.06
TOTAL		0.14
Fixed Costs
Administrative	30.00
Fixed Plant & Equipment	2,250.00
TOTAL	2,280.00

Therefore Trade off Point,

X * 0.23 + 1795 = X * 0.14 + 2280

or, 0.23X - 0.14X = 2280-1795

or, X = 485 / .09

or, X = 5,388.88 units

or, X = 5389 units

The Trade Off Point is 5389 units.

4. Since it can be seen that the Variable Cost per Unit is high and Fixed Cost is Low in System 1 hence for any quantity below 5389 units it is advisable to choose System 1 and since the variable cost per unit is low and Fixed Cost is high in System 2, hence for units above 5389 unit, System 2 is advisable.