1. A company has 3 plants and 4 warehouses. The supply and demand in units and corresponding transportation costs in ` Per unit are given below. On the basis of past experiences, following dispatch schedule has been finalized.
|
PLANTS |
Warehouses |
SUPPLY |
|||
|
(transportation cost in ` Per unit) |
CAPACITY |
||||
|
|
I |
II |
III |
IV |
(in units) |
|
A |
10 |
8 |
7 |
12 |
5000 |
|
|
|
5000 |
|
|
|
|
B |
12 |
13 |
6 |
10 |
6000 |
|
|
|
|
4500 | 1500 |
|
|
C |
8 |
10 |
12 |
14 |
9000 |
|
|
7000 | 500 |
|
1500 |
|
|
Demand (in units) |
7000 |
5500 |
4500 |
3000 |
20000 |
Answer the following questions with justification :
(i) Is the above solution optimal ? Find the optimal solution.
(ii) Calculate the total minimum transportation cost as per the optimal solution.
(iii) If the transport carrier offers 10% discount on route C to III, should the management accept the offer ? Analyze the optimal solution to find answer.
(Ans : (i) Solution is not optimal (ii) Minimum Tc = ` 1,62,500 (iii) Discount offer not accepted)
2. Cement Manufacturing Company wishes to transport cement from its three factories P, Q and R to five distribution depots situated at A, B, C, D, and E.
The quantities produced at the factories per week, requirements at the depots per week and respective transportation costs in ` Per tons are given in the table below.
|
Factories |
Depots |
Tons available |
||||
|
A |
B |
C |
D |
E |
|
|
|
P |
4 |
1 |
3 |
4 |
4 |
60 |
|
Q |
2 |
3 |
2 |
2 |
3 |
35 |
|
R |
3 |
5 |
2 |
4 |
4 |
40 |
|
Total Required |
22 |
45 |
20 |
18 |
30 |
135 |
Determine the least cost distribution programme for the company. If the transportation cost from R to D is changed to ` 2/- per ton, does this affect the optimal allocation ? if so, determine the revised schedule.
(Ans : Optimal cost ` 290/-, Revised Optimal cost ` 272/-)
3. Solve the following transportation problem to maximize profit and give criteria for optimality.
|
Origin
|
Destination Profit (in ` Per unit) |
Supply
|
|||
|
A B C |
1 40 44 38 |
2 25 35 38 |
3 22 30 28 |
4 33 30 30 |
100 30 70 |
|
Demand |
40 |
20 |
60 |
30 |
|
|
(Ans : Max. profit = ` 5130)
|
4. A company has 3 warehouses W1, W2, W3 from where it supplies products to 3 markets M1, M2, M3. Availability at warehouses is 2000, 1500 & 1000 units. Market requirements are 1200, 1800 & 1000 units.
Profit potential per unit from each warehouse to each market is as given below :
|
To |
M1 |
M2 |
M3 |
| From | |||
|
W1 |
25 |
22 |
23 |
|
W2 |
15 |
20 |
18 |
|
W3 |
18 |
17 |
16 |
Find optimal transportation schedule to maximize total profit.
(Ans : Max. profit = ` 86700)
5. A company supplies products from 3 warehouses to 3 markets. Supply at warehouses A, B and C is 2500, 1500 and 1000 units. Demand at markets P, Q and R is 2000, 1000 and 2000 units.
Profit per unit in (`) is :
|
To |
P |
Q |
R |
| From | |||
|
A |
20 |
30 |
25 |
|
B |
15 |
21 |
19 |
|
C |
12 |
16 |
14 |
Due to operational constraints, it is not possible be transport any quantity from warehouse B to market Q.
Determine optimal transportation schedule and optimal profit.
(Ans : Max. profit = ` 104000)
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