Bushwack Oil produces Regular and Premium gasoline from two types of crude oil: crude 1 and crude 2. Regular is allowed to contain up to 4% impurities, and Premium is allowed to contain up to 3% impurities. Regular sells for $72 per barrel, whereas Premium sells for $84 per barrel. Up to 4200 barrels of Regular and up to 4300 barrels of Premium can be sold. the cost per barrel of each crude, their availability, the level of impurities in each crude are shown below. Each barrel of Premium also requires an additive that costs $2.50 (its volume is insignificant).
|
Crude 1 |
Crude 2 |
| Cost per barrel |
$56 |
$65 |
| Impurity percentage |
10% |
2% |
| Availability |
4000 |
4500 |
Before blending the crude oil into gas, any amount of each crude can be "purified" at a cost of $3.50 per barrel. This purification eliminates half of the impurities in the crude oil.
- How many barrels of crude 1 and crude 2 should be mixed for Regular to maximize profit?
- How many barrels of crude 1 should be purified? How many of crude 2?