Q26 of 97 Page 1376

A brick manufacture has two depots, P and Q, with stocks of 30000 and 20000 bricks respectively. He receives order from three building A, B, C, for 15000, 20000 and 15000 bricks respectively. The costs of transporting 1000 bricks to the building from the depots are given below.


How should the manufacture fulfill the orders so as to keep the cost of transportation minimum?



Let x bricks be transported from P to A and y bricks be transported from P to B.


Therefore, 30000 - (x + y) will be transported to C.


Also, (15000 - x) bricks, (20000 - y) bricks and (15000 - (30000 - (x + y))) bricks will be transported to A, B, C from Q.


∴According to the question,


x


Minimize Z = 0.04x + 0.02(15000 - x) + 0.02y + 0.06(20000 - y) + 0.03(30000 - (x + y)) + 0.04((x + y) – 15000)


Z = 0.03x - 0.03y + 1800


The feasible region represented by x is given by



The corner points of feasible region are A(0,15000) , B(0,20000) , C(10000,20000) , D(15000,15000), E(15000,0).



The minimum value of Z is 1200 at point (0,20000).


Hence, 0, 20000, 10000 bricks should be transported from P to A, B, C and 15000, 0, 5000 bricks should be transported from Q to A, B, C.


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25

Two godowns, A and B, have a grain storage capacity of 100 quintals and 50 quintals respectively. Their supply goes to three ration shops, D, E and F, whose requirements are 60, 50 and 40 quintals respectively. The costs of transportation per quintal from the godowns to the shops are given in the following table.


How should the supplies be transported in order that the transportation cost is minimum?


 25

Two godowns, A and B, have a grain storage capacity of 100 quintals and 50 quintals respectively. Their supply goes to three ration shops, D, E and F, whose requirements are 60, 50 and 40 quintals respectively. The costs of transportation per quintal from the godowns to the shops are given in the following table.


How should the supplies be transported in order that the transportation cost is minimum?


 26

A brick manufacture has two depots, P and Q, with stocks of 30000 and 20000 bricks respectively. He receives order from three building A, B, C, for 15000, 20000 and 15000 bricks respectively. The costs of transporting 1000 bricks to the building from the depots are given below.


How should the manufacture fulfill the orders so as to keep the cost of transportation minimum?


 27

A medicine company has factories at two places, X and Y. From these places, supply is made to each of its three agencies situated at P, Q and R. the monthly requirement of the agencies are respectively 40 packets, 40 packets and 50 packets of medicine, while the production capacity of the factories at X and Y are 60 packets and 70 packets respectively. The transportation costs per packet from the factories to the agencies are given as follows.


How many packets from each factory should be transported to each agency so that the cost of transportation is minimum? Also, find the minimum cost.