$3$ A company must meet the following demands for a product: January, $30$ units; February, $30$ units; March. $20$ units. Demand may be backlogged at a cost of $$\frac{5}{?}$ unitimonth. All demand must be met by the end of March. Thus, if $1$ unit of January demand is met during March, a backlogging cost of $5(2)=$$$10$ is incurred. Monthly production capacity and unit production cost during each month are given in Table $66.$ A holding cost of $$20/$unit is assessed on the inventory at the end of each month.

a Formulate a balanced transportation problem that could be used to determine how to minimize the total cost $($including backlogging, holding, and production costs$)$ of meeting demand.