Linear programming: Give it a go
The company BioFuels Ltd makes fuels for cars and lorries. All of their fuels are sustainably manufactured from biomass.
BioFuel Ltd produces a E10 and E85 unleaded petrol.
- E10 unleaded petrol contains 90% traditional petrol, including octane, (typically from fossil fuels) and 10% bioethanol (from biomass).
- E85 unleaded petrol contains 15% traditional hydrocarbons, including octane, and 85% bioethanol.
| Bio-ethanol (per litre) | Octane (per litre) | Other hydrocarbons (per litre) | |
|---|---|---|---|
| E10 fuel | 100mL | 810mL | 90mL |
| E85 fuel | 850mL | 120mL | 30mL |
| Total available | 1500L | 6000L | 4000L |
E10 fuel is priced at £1.46 per litre and BioFuels Ltd makes £0.23 profit on each litre. The E85 fuel is prized at £1.97 per litre and BioFuels Ltd makes £0.46 profit on each litre.
BioFuels Ltd would like the maximise their profit.
Identify
Using the information above and the technique introduced in the previous activity, try and answer the following questions. Start by formulating the problem mathematically, then identify the feasible region.
- What is the best production plan for them to maximise their profit?
- How much E10 fuel should they make?
- How much E85 fuel should they make?
- What is their profit for the production plan?
- What is the best production plan for them to maximise their turnover?
- How much E10 fuel should they make?
- How much E85 fuel should they make?
- What is their turnover for the production plan?
Later in this activity, you will return to this example and think about environment impact of these production plans. You will also look at developing a production plan that minimises the environment impact.
Introduction to Technology-Assisted Decision-Making
Introduction to Technology-Assisted Decision-Making
Reach your personal and professional goals
Unlock access to hundreds of expert online courses and degrees from top universities and educators to gain accredited qualifications and professional CV-building certificates.
Join over 18 million learners to launch, switch or build upon your career, all at your own pace, across a wide range of topic areas.
