Answer:
The company have to sell 40 items each week to maximize its profit.
Step-by-step explanation:
The given profit function is
[tex]p(x)=-0.5x^2+40x-300[/tex] .... (1)
where, p is weekly profit in dollars and x is number of sold items.
In the given function leading coefficient is negative, it means it is a downward parabola and vertex of a down word parabola is point of maxima.
If a parabola is defined as
[tex]f(x)=ax^2+bx+c[/tex] .... (2)
then the function is maximum at [tex]x=-\frac{b}{2a}[/tex].
From (1) and (2) we get
[tex]a=-0.5, b=40, c=300[/tex]
[tex]x=-\frac{b}{2a}=-\frac{40}{2(-0.5)}=40[/tex]
The given function is maximum at x=40.
Therefore the company have to sell 40 items each week to maximize its profit.
