[填空题]
The owner of a bakery has found that the profit obtained from selling1dh/06giatjt 2n o9tk/l5kym x cakes /l m ty to6j9 n0igakt1d/52kh8uhg0g0jg, 8vis j 7vhis give0 vvgj7su g8gh ,hj08in by the function
where k is a positive constant and $x \geq 0$ .
1. Find an expression for $P^{\prime}(x)$ in terms of k and x ；P’(X)=c-$\frac{ax^2}{bk^2}$;a= ,b= ,c= .
2. Hence, find the maximum value of P in terms of k,The maximum value of P is k.
The owner knows that the bakery makes a profit of $\$ 873$ when they sell 30 cakes.
3. Find the value of k= .
4. Determine how many cakes the bakery should sell to maximize their profit,The bakery should sell cakes to maximise their profit.
5 . Sketch the graph of P , labelling the maximum point and x -intercepts.
6. Determine the maximum number of cakes the bakery can sell before they start losing money, the maximum number of cakes they can sell before they start losing money is .
