Exercise
- Define the terms used in LPP.
- Mention the advantages of LPP.
- What are the assumptions and limitations of LPP?
- A firm produces three products. These products are processed on three different machines. The time required manufacturing one unit of each of the three products and the daily capacity of the three machines are given in the table.
|
Machine
|
Time per unit (mins)
|
Machine capacity
Min /day
|
|
Product 1
|
Product 2
|
Product 3
|
|
M1
|
2
|
3
|
2
|
440
|
|
M2
|
4
|
-
|
3
|
470
|
|
M3
|
2
|
5
|
-
|
430
|
It is required to determine the daily number of units to be manufactured for each product. The profit per unit for product 1, 2 and 3 is Rs. 4, Rs. 3 and Rs. 6 respectively. It is assumed that all the amounts produced are consumed in the market. Formulate the mathematical model for the model.
- A chemical firm produces automobiles cleaner X and polisher Y and realizes Rs. 10 profit on each batch of X and Rs. 30 on Y. Both products require processing through the same machines, A and B but X requires 4 hours in A and 8 hours in B, whereas Y requires 6 hours in A and 4 hours in B. during the fourth coming week machines A and B have 12 and 16 hours of available capacity, respectively. Assuming that demand exists for both products, how many batches of each should be produce to realize the optimal profit Z?
- A firm manufactures headache pills in two sizes A and B. Size A contains 2 grains of aspirin, 5 grains of bicarbonate and 1 grain of codeine. Size B contains 1 grain of aspirin, 8 grains of bicarbonate and 6 grains of codeine. It is formed by users that it requires at least 12 grains of aspirin, 74 grains of bicarbonate and 24 grains of codeine fro providing immediate effect. It is required to determine the least number of pills a patient should take to get immediate relief. Formulate the problem as a standard LPP.