IB Maths AI SL 5.7 Optimization Questions

Practise defining variables and constraints in an optimisation model, finding and classifying extrema, and reporting the feasible optimum with units and assumptions.

Exam points

Define variables and constraints in an applied optimisation problem.
Use differentiation or technology to find and classify a maximum or minimum such as profit, cost or volume.
State the optimal value with units and explain domain, feasibility and modelling assumptions.

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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 $x \mathrm{~cm}$ .

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(a)

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

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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.

[ 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)

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.

Explain why the production manager is incorrect.

[ 1 ]

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IB Maths AI SL 5.7 Optimization Questions question 1

Question (a)

Question (b)

Question (c)