At the end of September $2021,$ Plains All American Pipeline L$.$P$.($PAA$)$ stock cost $$10$ per share, was expected to yield $7\%($calculated on the total value of PAA stock you bought$)$ per year in dividends, and had a risk index of $2\mathrm{.}0,$ while Chevron Corp $($CVX$)$ stock cost $$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 $$23,000$ to invest in these stocks and would like to earn at least $$1,310$ 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 $=$

Constraints

$<=23,000$

$>=1,310$

x $>=0,$ y $>=0$

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$,$ y$)$

$=$

largest x$-$value

$($x$,$ y$)$

$=$

The minimum value of r occurs at which corner point?

$($x$,$ y$)=$

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$)$ shares

What is the minimum total risk index?