In: Statistics and Probability
Tanura Co. is building a refinery to produce four products:
diesel, gasoline, lubricants, and jet fuel. The minimum demand (in
bbl/day) for each of these products is 14.000, 30.000, 10.000, and
8.000, respectively. Oman and Dubai are under contract to ship
crude to Tanura Co. Because of the production quotas, the new
refinery can receive at least 40% of its crude from Oman and the
remaining amount from Dubai. The specifications of the two crude
oils lead to different product mixes: One barrel of Oman crude
yields 0.2 bbl of diesel, 0.25 bbl of gasoline, 0.1 bbl of
lubricant, and 0.15 bbl of jet fuel. The corresponding yields from
Dubai crude are 0.1, 0.6, 0.15, and 0.1, respectively.
a. Formulate an LP that solves for the minimum capacity of the
refinery (in bbl/day) of Tanura Co. b. Solve the problem using
computer (show the computer output). c. What is the optimal
solution and what is the optimal value of the objective function?
d. Which constraints are binding? e. What will happen if the demand
of the diesel is reduced by 1,000 bbl/day? f. What will happen if
the demand of the gasoline is increased by 1,000 bbl/day?