5.7 OptimisationIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

What are the steps of an optimisation problem?
What is the profit function?
How do you eliminate a second variable?
A rectangle has perimeter 60 m and width x. What is its area?
Which rectangle has the greatest area for a fixed perimeter?
Cylinder with surface area S: write S.
Volume of a cylinder?
How do you confirm a stationary point is a maximum?
How can a GDC find an optimum?
What do you do with a solution outside the domain?
Why check the ends of the domain?
What must the final answer include?

Exam questions on 5.7 Optimisation

A rectangular garden has a perimeter of 60 m. Its width is $x$ metres.
Find the maximum area of the garden.2 marks
A factory produces $x$ tonnes of steel each day. The daily cost, $C$ thousand USD, is modelled by $C(x)=2x^2-48x+500$ .
The factory has a contract that requires it to produce between 15 and 30 tonnes per day. Find the minimum daily cost under this contract, in USD.2 marks
A square sheet of card has side 30 cm. A square of side $x$ cm is cut from each corner and the sides are folded up to make an open box with no lid, where $0<x<15$ . The volume of the box is $V$ cm³.
Show that $V=4x^3-120x^2+900x$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).