Linear Programming Problem with Example

...

X = 600/3

X = 200

- Similarly no 500ml bottle

3x + 2y

2(0) + 2Y

2Y

Y = 600/2

Y = 300

PACKING

X

Y

200

0

0

300

- To produce 500ml bottles and 1000ml bottles both 2 machine must be used so we need to find a solution that satisfies both constraints simultaneously.

- For that we have to develop graph using above date to find feasible region is where all constraints are satisfied.

[pic 1]

According to above graph inside region is feasible solution .but we need to find optimal solution from the many possible solution.

Using corner point solution method we can find best optimal solution in feasible aria

According to above graph the mathematical theory behind LP is that optimal solution must line at one of the corner point or extreme point in the feasible region.

So we select 3 corner point to find optimal solution of beyond era pvt ltd

Point A

X

Y

Z

3000

5000

FILING

2

4

720

X

120

PACKING

3

2

600

Y

120

Z

960000

Z= 3000X + 5000Y

= 3000(120) + 5000(120)

= 960000

POINT B

X

Y

Z

3000

5000

FILING

2

4

720

X

200

PACKING

3

2

600

Y

0

Z

600000

Z= 3000X + 5000Y

= 3000(200) +5000(0)

= 600000

POINT C

X

Y

Z

3000

5000

FILING

2

4

720

X

0

PACKING

3

2

600

Y

180

Z

900000

Z=3000X + 5000Y

= 3000(0) + 5000(180)

= 900000

According to above solution best product mix of beyond era pvt ltd is both tow boltless size production 120 pcs . it is pont A

- Analyzing Result

Beyond era pvt ltd is company the import 2 machine to product 500ml and 1000ml water bottles. But those 2 machine working hours are limiting factors. Filing machine only can work 12 hours per day and packing machine only can work 10 hours per day but according to their marketing team they have over demand for both size water bottles. Production capacity is limited but demand is unlimited so beyond era management looking for us best solution for this problem. They want maximize their profit using those limited factor .

We identify this is linear programming product mix problem we develop formulas and got solution using graphical method.

According to that their best production mix is

120 500ml bolltes pack and 120 1000ml bottles pack per day that is the optimal production mix they can product using those limiting factors to maximize their profit they can collect Rs 960000 profit per day producing that product mix .