Example $2\mathrm{.}2$ A company has two plants, each of which produces and supplies two products: A and B$.$ The plants can each work up to $16$ hours a day. In plant $1,$ it takes three hours to prepare and pack $1,000$ gallons of A and one hour to prepare and pack one quintal of B$.$ In plant $2,$ it takes two hours to prepare and pack $1,000$ gallons of A and $1\mathrm{.}5$ hours to prepare and pack a quintal of B$.$ In plant $1,$ it costs Rs $15,000$ to prepare and pack $1,000$ gallons of A and Rs $28,000$ to prepare and pack a quintal of B$,$ whereas in plant $2$ these costs are Rs $18,000$ and Rs $26,000,$ respectively. The company is obliged to produce daily at least $10$ thousand gallons of A and $8$ quintals of B$.$

Formulate this problem as an LP model to find out as to how the company should organize its production so that the required amounts of the two products be obtained at the minimum cost.