A logistics company is designing a new delivery route between two cities, A and B, that are 100 km apart. The route must include a stop at a service station located somewhere between the two cities. The company’s research indicates that the fuel consumption rate (in litres per km) for the delivery truck is affected by the distance travelled before and after the stop. Specifically, the fuel consumption rate before the stop is given by $0.0001x + 0.2$, where $x$ is the distance (in km) from city A to the service station. After the stop, the fuel consumption rate is given by $0.0002y + 0.1$, where $y$ is the distance (in km) from the service station to city B.
b. Analyse the function $F(x)$ to determine the distance $x$ from city A to the service station that minimizes the total fuel consumption for the delivery route. Justify that your answer is a minimum.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 3 marks, testing your understanding of Optimisation Problems. It falls under Calculus in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers limits, continuity, differentiability, differentiation, and anti-differentiation.
identification of local maximum/minimum values over an interval and application to solving optimisation problems in context, including identification of interval endpoint maximum and minimum values
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