and had a risk index of $2\mathrm{.}0,$ while Chevron Corp $($CVX$)$ stock cost $$100$ per share, was expected to yield $5\%$ per year in dividends, and had a risk index of $3\mathrm{.}0.$ You have up to $$26,000$ to invest in these stocks and would like to earn at least $$1,520$ in dividends over the course of a year. $($Assume the dividend to be unchanged for the year.$)$ How many shares of each stock should you purchase to meet your requirements and minimize the total risk index for your portfolio? $($Assume the total risk index is calculated by adding the products of each risk index and the associated number of shares.$)$

Let $x=$ number of PAA shares, let $y=$ number of CVX shares, and let $r=$ risk index. Determine the objective and the constraints needed to solve the problem.

Objective

$r=2x+3y$

Constraints

$$

$x26,000$

$1,520$

$x0,y0$

$$

Graph the feasible region and determine the coordinates of all corner points. $($Round your answers to the nearest integer.$)$

smallest $x-$value $(x,y)=(x)$

$(x,y)=(x)$

largest $x-$value $,(x,y)=(x)$ The minimum value of $r$ occurs at which corner point?

$(x,y)=(x)$

State the minimum value of $r.$

$r$

How many shares of each stock should you purchase to meet your requirements and minimize the total risk index for your portfolio?

Plains All American Pipeline L$.$P$.($PAA$)$ shares

Chevron Corp $($CVX$)$

$x$ shares

What is the minimum total risk index?