Sitara Manufacturing is planning to build at least one new plant, and three citi

Question

Sitara Manufacturing is planning to build at least one new plant, and three cities are being considered: Faisalabad, Multan and Lahore. Once the plant or plants have been constructed, the company wishes to have sufficient capacity to produce at least 38,000 units each year. The costs associated with the possible locations are given in Table. The constraints arc: (1) total production capacity is at least 38,000; (2) number of units produced at the Baytown plant is 0 if the plant is not built, and it is no more than 21,000 if the plant is built; (3) number of units produced at the Lake Charles plant is 0 if the plant is not built, and it is no more than 20, 000 if the plant is built; (4) number of units produced at the Mobile plant is 0 if the plant is not built, and it is no more than 19.000 if the plant is built. Formulate LP Model.

Explanation / Answer

Let us assume

Faisalabad site Baytown plant will produce = x quantity

Multam site Lake charles plant will produce = y quantity

Lahore site Mobile plant will produce = z quantity.

Then our objective would be minimize the cost and the

Objective function=(32x+340000)+(33y+270000)+(30z+290000)=32x+33y+30z+900000

Minimize cost=32x+33y+30z+900000

Constraints are

1.x>=0,x<21000

2.y>=0,y<20000

3.z>=0,z<19000

Total prodution capacity is atleast 38000.

Therefore x+y+z>=38000

x+y+x<60000

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