An oil company has two depots A and B with capacities of 7000 L and 4000 L respectively. The company is to supply oil to three petrol pumps, D, E and F whose requirements are 4500L, 3000L and 3500 L respectively, the distances(in km) between the depots and the petrol pumps is given in the following table:

Assuming that the transportation cost of 10 litres of oil is 1 per km, how should the delivery be scheduled in order that the transportation cost is minimum? What is the minimum cost?

Two godwons A and B have grain capacity of 100 quintals and 50 quintals resepectively. They supply to 3 ration shopts,D, E and F whose requirements are 60,50 and 40 quintals respectively. The cost of transportion per quintal from the godwons to the shops are given in the following table : How should the supplies be transported in order that transportation cost is minimum ? What is the minimum cost ?

There are two factories located at place P and the other the place Q. From these locations, a certain commodity is to be delivered to eachof the three depots situated A, B and C. the weekly requirement of the de-pots are respectively 5,5 and 4 units of the commodity while the production capacity of the factories at P and Q are respectively 8 and 6 units. The cost of transportation per unit is gien below. How many units should be transported from each factory to each depot in order that the transportation cost in minimum ? What whill be the minimum transportation cost ?

There is a factory located at each of the two places P and Q. From these locations a certain commodity is delivered to each of the three depots situated at A, B and C. The weekly requirements of the depots are respectively 5, 5 and 4 units of the commodity while the production capacity of the factories at P and Q are respectively 8 and 6 units. The cost of transportation per unit is given below. Formulate the above LPP mathematically in order thaet transportation const in minimum. Solve the I.P.P.

A medicien company has factories at two places A and B. From these places, supply is made to each of its three agencies situated at P,Q and R. The monthly requirements of the agencies are respectively 40,40 50 packets of its medicines, while the production of the factories at A and B are 60 and 70 packets respectively. The transportation cost (in Rs) per packet from the factories to the agencies are given below. Formulate the linear programming problem so that the cost of transportation is minimum .

Suppose the Government has decided to erect a new Electrical Power Transmission Substation to provide better power supply to two villages namely A and B . The substation has to be on the line l. The distances of villages A and B from the foot of the perpendiculars P and Q on the line l are B from the foot of the perpendiculars P and Q on the line l are 3 km and 5 km respectively and the distance between P and Q is 6 km. (i) What is the smallest length of cable required to connect the two villages. (ii) Find the equations of the cable lines that connect the power station to two villages.(Using the knowledge in conjunction with the principle of reflection allows for approach to solve this problem) .