1Glueco produces three types of glue on two different produc

1.Glueco produces three types of glue on two different production lines (line 1 and line 2). Up to seven workers can work on a line at a time. Workers are paid S 00 per week on production line 1, and S900 per week on production line 2. For a week of production it costs S1000 to set up production line 1, and 52000 to set up production line 2. During the week on a production line, each worker produces the number of units of glue shown in the table below. Each week at least 120 units of glue 1, at least 150 units of glue 2, and at least 200 units of glue 3 must be produced. (a) Formulate an integer -programming model to minimize the total cost of meeting weekly demands.

Solution

Here we need to minimize the total cost of meeting weekly demands.

Let x₁ denotes number of workers working on production line 1 and x₂ denotes number of workers working on production line 2.

So objective function will be z = (500 x₁ + 1000)+(900x₂ + 2000) = 500x₁ + 900x₂ + 3000

We want to minimize this objective function given the following constraints:

Each week atleast 120 units of glue1 , atleast 150 units of glue2 and atleast 200 units of glue3 must be produced.

Also using the given table we get,

20x₁ + 50x₂ >= 120

30x₁ + 35x₂? >= 150

40x₁ + 45x₂? >= 200

Also upto 7 workers can work on a line at a time so,

x₁ <= 7 and x₂ <= 7

So we can write the integer-programming model to minimize the total cost of meeting weekly demands as follows:

Minimize z = 500x₁ + 900x₂ + 3000 given the following constraints:

20x₁ + 50x₂ >= 120

30x₁ + 35x₂? >= 150

40x₁ + 45x₂? >= 200

x₁ <= 7 and x₂ <= 7