5.7 OptimisationIB Maths: Applications and Interpretation SL: Mind map

Exam questions on 5.7 Optimisation

1. A rectangular garden has a perimeter of 60 m. Its width is $x$ metres.
   Find the maximum area of the garden.2 marks
2. 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
3. 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