Sunco processes oil into two types of products: aviation fuel and heating oil. As part of the
Question:
Sunco processes oil into two types of products: aviation fuel and heating oil. As part of the manufacturing process, oil can be partially processed into a fuel that is 50% aviation fuel or 100% aviation fuel. When processing oil into heating oil, there are no partial amounts (i.e. the oil must be processed to complete heating oil; no partial composition). An LP program has been established to maximize profits for the production of the three types of oil: Ahalf = half aviation, A = Aviation, and H = heating oil. The LP is shown below: | |
OBJECTIVE: Maximize | |
$50 Ahalf + $85 A + $43 H | |
CONSTRAINTS (non-negativity assumed) | |
Ahalf + A + H <= 8000 | (number of total barrels) |
Ahalf + 1.55*A + 0.7*H <= 5000 | (available hours) |
Ahalf + A = 4000 | (barrel condition) |
Ahalf <= 3000 | (barrel condition) |
(a) Choose two of the constraints and translate how the constraint is being used when maximizing profit. Put the constraint into your own words. | |
(b) Use software to compute the maximum profit for the LP above. How much of each of the three types of oil should be created to maximize profits? | |
(c ) Originally, heating oil would create $43 of profit for Sunco. How much could Sunco increase this profit amount per heating oil, while maintaining the solution set found in (b)? In other words, which profits for H would ensure the same production amounts of oil from (b)? At what profit margin for heating oil should Sunco consider producing heating oil? | |
(d) Do any of the constraints have a slack / surplus? If so, which constraint. Explain whether the constraint has a slack or a surplus. I need step by step instructions using excel |