The Better Products Company has decided to initiate the production of four new products, using three plants that currently have excess production capacity. The products require a comparable production effort per unit, so the available production capacity of the plants is measured by the number of units of any product that can be produced per day, as given in the rightmost column of the table shown below. The bottom row gives the required production rate per day, to meet projected sales. Each plant can produce any of these products, except that Plant 2 cannot produce product 3. However, the variable costs per unit of each product differ from plant to plant, as shown in the table below:

a) Formulate this problem as a transportation problem by constructing the appropriate parameter table.

b) Find an initial BF solution using the Northwest Corner Rule.

Perform one iteration using the transportation simplex method and, indicate the leaving basic variable, the entering basic variable for the new BF solution, the values of all the basic variables for new BF solution and the value of the objective function.

Plant 123 2 3 Production rate Unit Cost (S) for Product 2 27 29 30 30 1 41 40 37 20 3 28 27 30 4 24 23 21 40 Capacity Available 75 75 45