Help with operations research exam$(30\%)$ Tom would like $3$ pints of home brew today and an addition $4$ pints of home brew tomorrow. Dick is willing to sell a maximum of $5$ pints total at a price of $$6\mathrm{.}00$ per pint today and $$5\mathrm{.}40$ per pint tomorrow. Harry is willing to sell a maximum of $4$ pints total at a price of $$5\mathrm{.}80$ per pint today and $$5\mathrm{.}60$ per pint tomorrow.

Tom wishes to know that his purchases should be to minimize his cost while satisfying his thirst requirements.

$($a$)(15\%)$ Formulate a linear programming model for this problem, including an objective function, decision variables, and constraints.

$($b$)(15\%))$ Formulate this problem as a transportation problem by constructing the appropriate parameter table.