Develop a linear program that Photon Technologies can use to determine how many units of each battery pack to produce at each plant to minimize the total production and shipping cost $($in dollars$)$ associated with the new contract. $($Assume P$1=$ number of PT$-100$ battery packs produced at the Philippines plant, P$2=$ number of PT$-200$ battery packs produced at the Philippines plant, P$3=$ number of PT$-300$ battery packs produced at the Philippines plant, M$1=$ number of PT$-100$ battery packs produced at the Mexico plant, M$2=$ number of PT$-200$ battery packs produced at the Mexico plant, M$3=$ number of PT$-300$ battery packs produced at the Mexico plant.$)$