1. R.K. Steel Manufacturing Company produces two items P1 and P2. It uses Sheet Metal, equipment and labour. Input – Output relationships, resources available are as follows:
|
Input |
Product requirement per unit |
Availability |
|||
|
P1 |
P2 |
||||
| Sheet Metal | 1 Sq. cm | 1 Sq. cm | 50 Sq. cm | ||
| Labour | 1 man hour | 2 man hours | 80 man hours | ||
| Equipment | 3 hours | 2 hours | 140 hours | ||
| Profit (`) | ` 4 per unit | ` 3 per unit | |||
How many units of P1 and P2 should be manufactured to maximize the profit of the company? Use graphical Method.
2. ABC Ltd. manufactures tables and chairs. They have just acquired a new workshop that can operate 48 hours a week. Production of a table will require 2 hours and a chair will require 3 hours of production time. Each table will contribute ` 40/- to profit while a chair contributes ` 80 /-. The marketing department has determined that maximum of 15 tables & 10 chairs can be sold every week. Formulate the linear programming model and determine the optimum product mix of tables and chairs that will maximize profits for the company, by using graphical method or simplex method of linear programming.
3. M/s Print Well Pvt. Ltd. are facing a tight financial squeeze and hence are attempting cost saving wherever possible. The current contract is to print a book in hard cover and in paperback. The cost of hard cover type is ` 600/- per 100 copies and ` 500/- per 100 copies of paperback type. The company decides to run their two printing presses PI and PII for at least 80 hours and 60 hours respectively every week. PI can produce 100 hard cover books in 2 hours and 100 paper backs in 1 hour. PII can produce 100 hard cover books in 1 hour and 100 paper backs in 2 hours. Determine how many books of each type should be produced to minimize costs. Use simplex or graphical method of linear programming.
4. GJ Bottling Ltd. have two bottling plants, one located at G and the other at J. Each plant bottles three soft drinks namely, A, B and C. number of bottles bottled per day is a follows :
|
Drink |
Plant at |
|
|
|
G |
J |
|
A |
1,500 |
1,500 |
|
B |
3,000 |
1,000 |
|
C |
2,000 |
5,000 |
A market survey indicates that during the next month, there will be demand of at least 20,000 bottles of A, at least 41,000 bottles of B and at least 44,000 bottles of C. The operating cost per day for plants at G and J are 600 and 400 rupees respectively. For how many days each plant is run next month to minimize operating costs, while still meeting the market demand? Use graphical method of Linear Programming.
5. Using simplex method to solve the following LPP and explain the solution.
Maximize Z = 6x1 – 2x2 Subject to: 2x1 – x2 \<2,
x1 \< 4,
x1, x2 >/ 0
hi, can someone solve the question number 4, concerning the bottling plants