Tom would like exactly 3 pints of home brew today and at least an additional 4 pints of home brew tomorrow. Dick is willing to sell a maximum of 5 pints total at a price of $2.40/pint today and $2.16/pint tomorrow. Harry is willing to sell a maximum of 4 pints total at a price of $2.31/pint today and $2.25/pint tomorrow.

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

a) Formulate the linear programming model for this problem, and construct the initial simplex tableau.

b) Formulate this problem as a transportation problem by constructing the appropriate cost and requirements table.

c) Use the northwest corner rule to obtain a basic starting solution for the transportation simplex method.

d) Use the Vogel Approximation to obtain a basic starting solution for the transportation simplex method.

e) Solve the problem using as a starting basic solution the least cost method and solve by using the transportation simplex method.