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 LP$-$

simplex method. Please define X$1$: production of premium blend $(kg)$; X$2$: production of regular blend $(kg).$