Problem $3(40$ points$)$

A hospital needs to purchase $5$ gallons of perishable medicine for use during the current month

and $2$ gallons for use during the next month. Because the medicine is perishable, it can only be

used during the month of purchase. Two companies, Efe and Ada, sell the medicine. The

medicine is in short supply. Thus, during the next two months, the hospital is limited to buying at

most $3$ gallons from each company. Efe charges $$800$ per gallon during the current month and

$$600$ per gallon during the next month. Ada charges $$500$ per gallon during the current month

and $$450$ per gallon during the next month. The hospital wants to minimize the cost of

purchasing the medicine while satisfying its need.

$($a$)$ Formulate this problem as a transportation problem by constructing the appropriate

parameter table where column $j$ represents the month and row i represents the medicine

seller$/$supplier$.$