Question

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-

Answer 1

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