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

Ahalf + 1.55*A + 0.7*H <= 5000

Ahalf + A = 4000

Ahalf <= 3000

(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.