We need to ship a single product from two plants to two warehouses, and then from these two warehouses to three customers. The two plants are p$1$ and p$2$ Plant p$2$ has an annual capacity of $60,000$ units. The two plants have the same production costs. The two warehouses are w$1$ and w$2$ with identical warehouse handling costs. The three customers are c$1,$ c$2$ and c$3$ with demands of $50,000,100,000$ and $50,000,$ respectively. Products are shipped from the plants to the warehouses, and from the warehouses to the customers. Let x $($p$1,$ w$1)$