6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f7935caa-6626-4ba8-87ef-e9bb59e1ac3e-12_599_1084_292_486}
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\caption{Figure 1}
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A company makes a particular type of children's toy.
The annual profit made by the company is modelled by the equation
$$P = 100 - 6.25 ( x - 9 ) ^ { 2 }$$
where \(P\) is the profit measured in thousands of pounds and \(x\) is the selling price of the toy in pounds.
A sketch of \(P\) against \(x\) is shown in Figure 1.
Using the model,
- explain why \(\pounds 15\) is not a sensible selling price for the toy.
Given that the company made an annual profit of more than \(\pounds 80000\)
- find, according to the model, the least possible selling price for the toy.
The company wishes to maximise its annual profit.
State, according to the model, - the maximum possible annual profit,
- the selling price of the toy that maximises the annual profit.