IB Maths AI SL 5.7 Optimization Question Bank

Practise IB Mathematics SL/HL 5.7 by applying optimization methods to exam-style questions.

[Maximum number: 5]

A hollow chocolate box is manufactured in the form of a right prism with a regular hexagonal base. The height of the prism is $h \mathrm{~cm}$ , and the top and base of the prism have sides of length $x \mathrm{~cm}$ .

Figure for Question SL 5.7—Optimization question 1 — IB Maths AI SL

(a)

Find the value of x which maximizes the volume of the box.

[ 2 ]

from the graph of V or $\frac{\mathrm{d} V}{\mathrm{~d} x}$ OR solving $\frac{\mathrm{d} V}{\mathrm{~d} x}=0$

x=8.77(8.77382 \ldots)

(b)

Hence, or otherwise, find the maximum possible volume of the box.

The box will contain spherical chocolates. The production manager assumes that they can calculate the exact number of chocolates in each box by dividing the volume of the box by the volume of a single chocolate and then rounding down to the nearest integer.

[ 2 ]

from the graph of V OR substituting their value for x into V
$V_{\text {max }}=3040 \mathrm{~cm}^{3}(3039.34 \ldots)$

(c)

Explain why the production manager is incorrect.

[ 1 ]

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SL 5.7—Optimization question 1

Question (a)

Question (b)

Question (c)