An ice cream company produces 3 types of ice cream: regular, premium and supreme. Regular ice cream sells for $15/gallon, Premium for $25/gallon and Supreme for $30/gallon. The company ships its ice cream using its own little truck with capacity of 480 cubic units of space. Each gallon of regular, premium and supreme ice cream takes up 3, 4 and 5 cubic units respectively. The company has 640 litres of milk available. Regular, premium and supreme ice cream require 6, 6 and 7 litres of milk per gallon respectively. The company's objective is to maximize its operation revenue.

(a) Formulate the problem as a linear program and solve it using the simplex method in tabular form.

(b) If the manager decides to reduce the price of the supreme ice cream to $25/gallon, i.e., the same price as the premium, determine the new optimal solution using sensitivity analysis.