The Bubbly Soda (BS) Company produces popular sodas. A special type of soda consists of regular and diet soda. The company has received an order for a minimum of 400,000 litres of the special type. The customer specified that the order must contain at least 40% of regular soda and not more than 250,000 litres of diet soda. The customer also specified that the blend should be mixed in the ratio of 2 parts regular to 1 part diet. The BS Company can produce 500,000 litres per week, regardless of the blend. The production manager wants to complete the order in 1 week. The blend is sold for $12 per litre. The BS company's cost per litre is $4 for regular and $2 for diet. The company wants to determine the blend mix that will meet customer requirements and maximize profits.

a. Formulate algebraically a linear programming model for this problem (6 marks)

b. Solve this problem using Excel (6 marks)