A fertilizer company mixes three different types of chemicals in their Premium blend which sells for

$$\frac{1\mathrm{.}0}{k}g.$ Their less expensive blend $($Regular$)$ sells for $$\frac{0\mathrm{.}80}{k}g$ and contains only two types of

chemicals. The mixing formula for both blends is shown below.

The remainder of each blend is inert filler material which comes from nearby pit mine at a cost of

$$\frac{0\mathrm{.}10}{k}g.$ An unlimited supply of filler is available. The cost per $kg$ of type A$,$ type B and type C

chemicals is $$0\mathrm{.}30,$$$0\mathrm{.}25,$ and $$0\mathrm{.}21,$ respectively. Determine the optimal amount of each blend that

should be prepared for maximum profit; leftover chemical can be used again. Solve using LPsimplex

method. Please define X$1$: production of premium blend $(kg)$;$x2$ : production of regular blend $(kg).$