John produces three types of glue on two different production lines. Each line c

Question

John produces three types of glue on two different production lines. Each line can be utilized by up to seven workers at a time. Workers are paid $50 per week on production line, and $90 per week on production line 2. For a week of production it costs $100 to set up production line 1 and $200 to set up production line 2. During a week on a production line, each worker produces the number of units of glue shown 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. Formulate an IP to minimize the total cost of meeting weekly demands.

Explanation / Answer

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

Related Questions

Navigate

• Browse (All)
• Browse J
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.