A beekeeper’s hives are making Honey at a constant rate. The profit from honey can be represented by the equation

P(t)= -16t^2 + 2050t +150, where t is the time in days and P(t) is the profit the beekeeper receives. After how many days should she harvest her honey to maximize profit?

A: 4212100
B: 2050
C: 150
D: 64

P(t)= -16t^2 + 2050t +150, where t is the time in days and P(t) is the profit the beekeeper receives. After how many days should she harvest her honey to maximize profit?

A: 4212100

B: 2050

C: 150

D: 64

P(64)= -16(64)^2 + 2050(64) +150 = -16 * 4096 + 131200 + 150 = 65814

P(150)= -16(150)^2 + 2050(150) +150 = -16 * 22500 + 307500 + 150 = -52350

P(64)= -16(2050)^2 + 2050(2050) +150 = -16 * 4202500 + 4202500 + 150 = -63 037 350

The only is positif, it’s 64 days

MrRoyal MrRoyal · Answer 2 · 2021-10-01T14:20:10+02:00

The profit function is an illustration of a quadratic function.

Her harvest would be at maximum after 64 days

The function is given as:

[tex]P(t) = -16t^2 + 2050t + 150[/tex]

The maximum of a quadratic function is:

[tex]x = -\frac b{2a}[/tex]

In

[tex]P(t) = -16t^2 + 2050t + 150[/tex]

[tex]a = -16[/tex]

[tex]b = 2050[/tex]

So, the maximum is calculated as:

[tex]t = -\frac{b}{2a}[/tex]

This gives

[tex]t = -\frac{2050}{2 \times -16}[/tex]

[tex]t = \frac{2050}{2 \times 16}[/tex]

[tex]t = \frac{2050}{32}[/tex]

[tex]t = 64.0625[/tex]

Approximate

[tex]t = 64[/tex]

Hence, her harvest would be at maximum after 64days

Read more about maximum of a function at:

https://brainly.com/question/13581879