3) Sunco processes oil into two types of products: aviation fuel and heating oil
ID: 458192 • Letter: 3
Question
3) 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.
3) 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.
Explanation / Answer
a) Three type of products - Ah, A & H
Thier profit contribution per unit is $50per unit Ah, 85 per unit A and $ 43 per unit H.
Maximum profit comes from A oil. second max profit come from Ah.
Our focus should on A & Ah to maximize the profit within the given resource limitation.
The constraint related to total quantity QAh + A = 4000.
Profit per unit from A and Ah is relatively high, so meet this constraint
Ah + A = 4000
Next constriant is time related :We should use max available hours to maximize the profit
1Ah + 1.55 A+0.7 <= 5000
b)
Solution :Max Profit = $ 23636
Quantities we need produce at Max Profit :
Ah = 2181.8 barrels
A = 1818.2 barrels
H= 0 barrels
Sensitivity Analysis:
c) We can increase the profit of H oil from $43 to 44.545 without changing our total profit i.e 4263636.
if the H oil profit /unit > $ 44.5454, we can produce H oil becuase it starts contributing to the profit.
d).First constraint is total production : Ah +A + H < 8000 barrels
But our solution is only producing Ah + A = 4000 barrels
We can increase 4000 barrels additional production
4th Constraint having surplus
Maximum limit for Ah is < 3000 and only produced 2181.8 and we add 818.2 barrels more Ah production.
Ahalf A H Units in barrels 2181.8 1818.2 0.0 Hours 1 1.55 0.7 Profit/unit 50 85 43 Constraints Barrel oil 4000 <= 8000 Total hours 5000 <= 5000 Barrel 4000 = 4000 barrel 2181.818 <= 3000 Condition Non -Ve Objective function 263636Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.