Question

Hi how are you today can you please help me with this question

Answer 1

(a) From the graph we get that the points (100, 30 000) and (200, 30 000) are on the parabola, therefore the largest possible value of x such that the are is 30 000 m² is

`200\text{ m.}`

(b) To find the largest possible area we calculate the vertex of the parabola.

Taking the given equation to its standard form we get:

`\begin{gathered} A=-1.5(x^2-300x)=-1.5((x-150)^2-150^2), \\ A=-1.5(x-150)^2+33\text{ 750.} \end{gathered}`

Therefore, the coordinates of the vertex are:

`(150,33750)\text{.}`

From the vertex we get that, the value of x that maximizes the area is x=150.

Substituting x=150 in 3x+2y=900, and solving for y, we get:

`\begin{gathered} 450+2y=900, \\ 2y=450, \\ y=225. \end{gathered}`

The values of x and y that maximize the area are x=150m, y=225 m.

(c) From the previous step we get that the maximum area of the paddock is 33 750 m².