Operations Research Answers

Best sell LTD has decided to launch a new product in addition to it's range of products. The following information is provided.

1) The New product may be distributed through any combination of the two company warehouse W1 and W2

2) The available monthly production capabilities for the new products are;

1000 units at plant A

2000 units at plant B

1000 units at plant C

3) Three major concentration points of customer demands are at location E,F qand G which are estimated to have a monthly demand of :

900 units at plant E

800 units at plant F

900 units at plant G

4) The unit production costs amount to sh30, sh40, sh 10 at A, B and C.

5) The unit transportation costs from plant to warehouse and unit delivery cost from warehouse to customer as shown below

Transportation cost schedule

Plants. W1. W2

Sh sh

A. 60. 60

B. 50. 50

C. 130. 40

Delivery cost schedule

Warehouse. E. F. G

Sh sh. Sh

W1. 30 60. 80

W2. 5-. 50 90

A team of 15 men is employed to unload lorries at a terminal. The team works a -6 hour day during which 36 lorries arrive (i.e 6 per hour)and it takes 7.5 minutes to attend one lorry with the team acting as a single unit. Lorries are served on a FIFO basis. It has been estimated that the cost of keeping lorries waiting is $6per hour. Members of the teams are each paid $2.50 per hour. It had been estimated that if the size of the team is increased to 20 men, the average service time would fall to 5 minutes.

Reguired

Calculate the cost of the present system and the cost of the proposed system, and determine whether an increase in the size of the team would be justified on grounds of cost.

1.   In each of the following situations, identify the customer and the server:

(a) Planes arriving at an airport.

(b) Taxi stand serving waiting passengers.

(c) Tools checked out from a crib in a machining shop.

(d) Letters processed in a post office. 

2A firm manufactures two products A and B on which the profits earned per unit are Rs. 3 and Rs.4 respectively. Each product is processed on two machines M and M Product Arequires one minute of processing time on M, and two minutes on M, while requires one minute on M, and one minute on M, Machine M is available for not more than 7 hours 30 minutes while machine M is available for 10 hours during any working day. Find the number of units of products A and B to be manufactured to get maximum profit. Formulate the above as a LPP and solve by graphical method.