Programming

Operations Research

Unit $2$

$6.$ Three grades of coal A$,$ B$,$ and C contain ash and phosphorous as impurities. In a particular industrial process, a fuel obtained by blending the above grades containing not more than $25\%$ ash and $0\mathrm{.}03\%$ phosphorous is required. The maximum demand of the fuel is $100$ tons. Percentage impurities and costs of the various grades of coal are shown below. Assuming that there is an unlimited supply of each grade of coal and there is no loss in blending, formulate the blending problem to minimise the cost.

$\backslash$table$[[$Coal grade,Ash$\%,$Phosphorus$\%,$Cost per ton in Rs$.],[$A$,30,0\mathrm{.}02,240],[$B$,20,0\mathrm{.}04,300],[$C$,35,0\mathrm{.}03,280]]$