Question

Could anyone please provide some guidance to this linear programming model. Not after an answer, just how I can approach this. Thanks.

A mining town has three districts. The number of skilled and unskilled workers in each district is given in the following table. Of all the workers, 25% are unskilled workers District 1 2 Unskilled Workers 50 50 100 Skilled Workers 200 250 150 There are two current sites being mined by the mining company. Both of the current mining sites must have approximately the same percentage of unskilled workers (within 5%) as the entire workforce in the mining town. The distances (in kilometres) between the districts and the two current mining sites are shown in the following table Site 2 District 1 2 3 Site 1 Each site must have between 300-500 workers (inclusive). The company wishes to determine an assignment of workers that minimises the total distance workers must be transported (travel) to site each day

Answer 1

Per the first table, there are 800 workers available in the mining town (200 unskilled & 600 skilled).

The objective is to minimise the total distance workers that the workers travel to the two sites each day, assuming 300 to 500 workers at each site everyday. Both the mining sites must have same percentage of unskilled workers as the entire workforce.

So the entire workforce is 800, of which 200 are unskilled, so to depute same percentage of them at both sites, 100 unskilled persons must be deployed each. This means that we need to allocate 300 more workers at both sites. So we would have 400 workers at each site.

If x1 is the distance between D1(district 1 ) & S1 (Site 1) & x2 for D2 & S1, the matrix would look like:

District to Site Distance	S1	S2
D1	x1	2x4
D2	2x2	x5
D3	x3	x6

The equations would look like:

Minimise distance:

x1+2x2+x3>=400

2x4+x5+x6>=400