A transportation problem $(20$ points$)$ A company wants to minimize the cost of shipping a product from $2$ different factories to $4$ different customers. The cost of shipping $($$ per unit$),$ supply, and demand is shown in the following table, Factory $1$ $$2\mathrm{.}25$ Origins $$1\mathrm{.}50$ $$2\mathrm{.}0050000$ Customer $1$ Customer $2$ Customer $3$ Customer $4$ Supply $$1\mathrm{.}75$ Factory $2$ $$2\mathrm{.}00$ $$2\mathrm{.}50$ $$2\mathrm{.}50$ Demand $$1\mathrm{.}5030,00023,0005000015,00032,000$ How should the company distribute the products to minimize the cost of shipping? Formulate & solve the linear programming model about transportation. $(1)$ Formulate