A dealer in rural area wishes to purchase a number of sewing machines .. He has only Rs- 5,760 to invest and has space for at most 20 items for storage- An electronic se.ving machine costs him Rsv 36 and manually operating sewing machine Re. 240. He can sell an electronic seguing machine at a profit of Rs. 22 and a manually operated eewing machine at a profit of Rs- 18- Assuming that he can sell all the items that he can buy, hoe should he invest his money in order to maximize his profit? Make it as a LPP and solve it graphically-
Answers
Answer:
Max profit is with 8 Electronics + 12 Manual Sewing Machines of Rs 392
Step-by-step explanation:
A dealer in rural area wishes to purchase a number of sewing machines .. He has only Rs- 5,760 to invest and has space for at most 20 items for storage- An electronic se.ving machine costs him Rsv 36 and manually operating sewing machine Re. 240. He can sell an electronic seguing machine at a profit of Rs. 22 and a manually operated eewing machine at a profit of Rs- 18- Assuming that he can sell all the items that he can buy, hoe should he invest his money in order to maximize his profit? Make it as a LPP and solve it graphically-
Amount to invest = Rs 5760
Electronic Sewing Machine = E
Manual operated sewing machine = M
E + M ≤ 20
E ≤ 20 & M ≤ 20 - eq 1
360 E + 240 M ≤ 5760
=> 3E + 2M ≤ 48
E ≤ 16 & M ≤ 24 - eq 2
from eq 1 & eq2
E ≤ 16 & M ≤ 20
Profit
22E + 18M
Considering Extreme cases
M = 20
Profit = 18 * 20 = Rs 360
E = 16
Profit = 22* 16 = Rs 352
We can draw a graph with table
E M Profit (22E + 18M)
16 0 352
15 1 348
14 3 362
13 4 358
12 6 372
11 7 368
10 9 382
9 10 378
8 12 392
7 13 388
6 14 384
5 15 380
4 16 376
3 17 372
2 18 368
1 19 364
0 20 360
Max profit is with 8 Electronics + 12 Manual Sewing Machines of Rs 392