The document describes a project using linear programming to determine the optimal production levels of four types of UPS (400V, 875V, 1025V, and 1550V) given resource constraints. The objective is to maximize total profit. The solution found that producing 300 units of 875V UPS maximizes profit at Rs. 75,000. A sensitivity analysis showed that battery, plug socket, and transformer constraints were not binding and their usage could be increased, but fuse constraint was binding and its usage could only be increased by 175 units before impacting the optimal solution.

1. MANAGEMENT SCIENCE
Project Report
Submitted to Management Department,
ITM University, Gwalior
For the Fulfillment of 3rd Trimester
SUBMITTED TO:-
SUBMITTEDD BY:-
SUBMITTEDD BY:-
PUNEET GUPTA
PUNEET GUPTA
PRADEEP KUMAR
PRADEEP KUMAR
MD ATTULLAH
MD ATTULLAH
MANISH SINGH
MANISH SINGH
SAGAR JADHAV
SAGAR JADHAV

2. introduction
• We are making an operations Research
project using Linear Programming to take
decision what type of UPS we have to make
more which utilize our full resources and will
help to increase our profit.

3. Data
UPS TYPE 400volt 875volt 1025volt 1550volt Available
Bettery constraint 1 2 3 4 <= 950
plug socket 2 2 4 4 <= 1150
fuse 1 1 2 2 <= 300
transfamer 1 1 2 3 <= 550

4. Basically we have four type of UPS 400VOLT, 875 VOLT, 1025 VOLT,
1550 VOLT
we have to use 1 battery in 400 VOLT UPS, 2 Battery in 875 VOLT UPS,
3 Battery in 1025VOLT UPS, 4 Battery in 1550VOLT UPS. From the
available battery (i.e.- 950)
we have to use 2 Plug Socket in 400 VOLT UPS, 2 Plug Socket in 875
VOLT UPS, 3 Plug Socket in 1025VOLT UPS, 4 Plug Socket in 1550VOLT
UPS. From the available Plug Socket (i.e.- 1150)
we have to use 1 Fuse in 400 VOLT UPS, 1 Fuse in 875 VOLT UPS, 2
Fuse in 1025VOLT UPS, 3 Fuse in 1550VOLT UPS. From the available
Fuse (i.e.- 300)
we have to use 1 trans farmer in 400 VOLT UPS, 1 Trans farmer in 875
VOLT UPS, 2 Trans farmer in 1025VOLT UPS, 3 Trans farmer in
1550VOLT UPS. From the available Trans farmer (i.e.- 550)

5. • We have gaining unit profit Rs 200 for
400VOLT UPS, Rs 250 for 875VOLT UPS, Rs 350
for 1025 VOLT UPS, Rs 500 for 1550 VOLT UPS

6. Constraint and Objective Function
By the above Data Our Constraint is :-
1X 2X1 3X3 4X4 <=950
2X 2X 3X3 4X4 <=1150
1X 1X 2X3 2X4 <=300
1X 1X 2X3 3X4 <=550
(Objective Function)Z=
200X+250X2+350X3+500X4

7. Solution by Solver
objective
0 300 0 0
function
Unit Profit 200 250 350 500 75000
Availab
UPS TYPE 400volt 875volt 1025volt 1550volt used
le
Bettery
1 2 3 4 600 <= 950
constraint
plug socket 2 2 4 4 600 <= 1150
fuse 1 1 2 2 300 <= 300
transfamer 1 1 2 3 300 <= 550

8. Senstivity Report
Microsoft Excel 14.0 Sensitivity Report
Worksheet: [Book1]Sheet1
Report Created: 29-May-12 10:01:09 AM
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$E$4 objective function 0 -50 200 50 1E+30
$F$4 objective function 300 0 250 1E+30 0
$G$4 objective function 0 -150 350 150 1E+30
$H$4 objective function 0 0 500 0 1E+30
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$I$8 Bettery constraint used 600 0 950 1E+30 350
$I$9 plug socket used 600 0 1150 1E+30 550
$I$10 fuse used 300 250 300 175 300
$I$11 transfamer used 300 0 550 1E+30 250

9. Interpretation
• According to Sensitivity Report:-
• In Constraint View:-
• Battery, Plug Socket, Transfarmer have ‘0’
shadow Price that’s mean these are not Binding.
We increase these constraint up to ‘1E+30’ as
(allowance increase is 1E+30) . They will not
effect the optimum solution because they have
slack value( resource that are unused):- 350 for
Battery,550 for Plug Socket,250 for Transfarmer.

10. • If we talk about Wire than it is not binding its
shadow price is 250.
• It’s Allowable increase is 175 so we increase
the use of wire up to 140. After increasing of
140 it will effect the optimum solution with
250/unit.
• It’s Allowable Decrease is 300 so We can
Decrease it up to 300 after that it will effect
the optimum solution.

11. Variable Cell:-
Reduced Cost
The amount an objective function coefficent must change before we
would make any of the product.
or, the amount the profit would change if you made at least one unit of
the product x
200 was not a high enough profit on 400VOLT UPS to make any. Its
profit must increase to 200+50or 250 before we would make 400VOLT
UPS . [ reduced cost is -50 . till 50 unit cost is valid after this we cannot
say.
For Product X3 1025VOLT UPS )= profit must increase to 350+150=500
[ reduced cost is -150 . till 150 unit cost is valid after this we cannot
say.
We are already making 875VOLT UPS , so their reduced costs are 0.