Q39. - Algebra 2

Question

Carl Talbert estimates that he will need to earn at least  $9000$ per year combined in dividend income from two stocks he owns to spplement his retirement plan

We have to check whether he can make enough from $3000$ enough from shares of each company or not.

Step-by-Step Solution

Answer

The answer is no he cannot make enough from $3000$shares of each company.

Step-1 – Describing the given inequality.

Consider the following inequality $1.2x+1.3y\ge 9000$

boundary in the graph of the inequality $1.2x+1.3y\ge 9000$ the inequality Since, the inequality sign is $\ge$ the boundary is solid.

Consider the point of origin $\left(0,0\right)$ on substituting the value in inequality as

$\begin{array}{l}1.2x+1.3y\ge 9000\\ 1.2\left(0\right)+1.3\left(0\right)\ge 9000\\ 0\ge 9000\end{array}$

Here the origin does not satisfy the inequality, therefore the shaded region not containing the origin point.

Therefore, the all points lying above the solid boundary satisfies the inequality.

Since, value of both the coordinate cannot be negative it is shaded only in the first quadrant.

Step-2 – Plot the graph of the given function

The graph can be plot in inequality and it is shown in form of area above the shaded region as follows:

Step-3 – Substitute the value in the inequality.

By putting the value $x=3000$and $y=3000$in above inequality as

$\begin{array}{l}1.2x+1.3y\ge 9000\\ 1.2\left(3000\right)+1.3\left(3000\right)\ge 9000\\ 3600+3900\ge 9000\end{array}$

Therefore, 

$7500\ge 9000$ Which is not true Hence, the answer is No.