A Syringe Manufacturer Has Three Plants P$1,$ P$2$ And P$3$ From Which The Syringes Need To Be Transported To Four Demand Destinations D$1,$ D$2,$ D$3,$ D$4.$ The Supply Capacities Of The Three Plants Are $4\mathrm{.}5,6\mathrm{.}2$ And $3\mathrm{.}8$ Million Units Respectively,A syringe manufacturer has three plants P$1,$ P$2$ and P$3$ from which the syringes need to be transported to four demand destinations D$1,$ D$2,$ D$3,$ D$4.$ The supply capacities of the three plants are $4\mathrm{.}5,6\mathrm{.}2$ and $3\mathrm{.}8$ million units respectively, while the demands of the four markets are $3\mathrm{.}1,3\mathrm{.}2,2\mathrm{.}4$ and $4\mathrm{.}9$ million units respectively. Since the road from P$2$ to D$2$ is under renovation, it cannot be used currently. And the customers of demand destination D$3$ have stated that they want atleast half of their demand to be met from Plant P$2.$ The logistics manager has to optimally meet the demand of all the markets at minimum overall $25$ cost$.$ Given the transportation cost per unit matrix between the different plants and demand markets as below, formulate the suitable linear programing model for the logistics manager.