Answer:
The number of elephant ears that must be sold to maximize profit is 400.
Step-by-step explanation:
Given that,
The profit that a vendor makes per day is given by
P(x)= - 0.004x² +3.2 x -200
where x is number of elephant ears.
P(x)= - 0.004x² +3.2 x -200
Differentiating with respect to x
P'(x)= - 0.008x+3.2
Again differentiating with respect to x
P''(x) = -0.008
For maximum or minimum P'(x)=0
- 0.008x+3.2=0
⇒0.008x=3.2
[tex]\Rightarrow x=\frac{3.2}{0.008}[/tex]
⇒ x = 400
[tex]P''(x)|_{x=400} = -0.008<0[/tex]
Since at x=400, P''(x)<0, the profit is maximize.
P(400) = -0.004×400²+3.2×400-200
=440
The number of elephant ears that must be sold to maximize profit is 400.
