Question

Carrington Oil produces gas I and gas 2 from two
types of crude oil: crude I and crude 2. Gas I is allowed
to contain up to 4% impurities. and gas 2 is allowed
to contain up t<> 3% impurities. Gas I sells for
$8 per barrel, whereas gas 2 sells for $ 12 per barrel.
Up to 4200 barrels of gas 1 and up to 4300 barrels of
gas 2 can be sold. The cost per barrel of each crude,
their availability. and the level of impurities in each
crude arc listed in the fileP04_67.xls. Before blending
the crude oil into gas, any amount of each crude
can be "purified" for a cost of $0.50 per barrel. Purifi cation
eliminates half of the impurities in the
crude oil.
a. Determine how to maximize profit.

Data on crudes
	Crude 1	Crude 2
Cost per barrel	$6	$8
Impurity percentage	10%	2%
Availability	5000	4500
Purification cost per barrel	$0.50
Percent impurities eliminated	50%
Data on types of gas
	Unit price	Max impurity	Max sales
Gas 1	$8	4%	4200
Gas2	$12	3%	4300

Answer 1

Each of the crude type can be either used directly or can be used after the purification at an additional charge of $0.5.

Let be the gallons of crude i used as is to produce gas j, and be the gallons of crude i used after purification produce gas j, where i=1,2 and j=1,2

These are the decision variables.

The total gallons of gas 1 produced is and gallons of gas 2 produced is

The total revenue earned is

The total cost of crude 1  used as is @ $6 per gallon is

The total cost of crude 1  used after purification @ $6.5 per gallon is

The total cost of crude 2 used as is @ $8 per gallon is

The total cost of crude 2 used after purification @ $8.5 per gallon is

The net profit is revenue - total cost

We want to maximize this, hence this is the objective function

Now the constraints

Gas I is allowed to contain up to 4% impurities

and gas 2 is allowed to contain up to 3% impurities.

Up to 4200 barrels of gas 1 can be sold.

and up to 4300 barrels of gas 2 can be sold.

A total of 5000 gallons of crude 1 is available, hence total crude 1 used cannot be greater than this

A total of 4500 gallons of crude 2 is available, hence total crude 2 used cannot be greater than this

The LP model is

Maximize

s.t.

Prepare the following sheet

get this

setup data--->solver

get this

The blend that can maximize the profit is

	Crude 1	Crude 1 Purified	Crude 2	Crude 2 Purified
Gas 1	0.0	3150.0	0.0	1050.0
Gas 2	0.0	1433.3	2866.7	0.0