Question: The buyer of a large tobacco manufacturer has the choice of four tobacco types Virginia, Burley, Latakia, and Kentucky. Once sufficient quantities have been purchased, they will make three blends of pipe tobacco, viz., Sweet Smell, Brown Lung, and Black Death. The following information is available.
• The four types of tobacco cost $3, $6, $5, and $2 per pound (in the order they were mentioned).
• The final blends are sold by the 4 oz pouch, i.e. there are four pouches per pound.
• The blends sell for $7, $9, and $12 per pouch (in the above order).
• Sweet Smell consists of 20 % Virginia, 50 % Burley, and 30 % Latakia, Brown Lung is blended from 40 % Latakia and equal proportions of the remaining tobaccos, and Black Death is 80 % Kentucky and 20 % Latakia.
• The four tobaccos are available in limited quantities. We may purchase up to 300 lbs of Virginia, 500 lbs of Burley, 100 lbs of Latakia, and 50 lbs of Kentucky.
• Our customers have placed orders for exactly 500 pouches of Sweet Smell and 400 pouches of Brown Lung. There are no firm orders for the expensive Black Death, but we expect to be able to sell between 80 and 120 pouches.
(a) Formulate a linear programming problem for the above situation. Define the variables clearly.
(b) Assume that there is a 5 % loss in the blending process. Explain the changes in the formulation.