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 2.0, while Chevron Corp (CVX) stock cost $100 per share, was expected to yield 5% per year in dividends, and had a risk index of 3.0. You have up to $33,000 to invest in these stocks and would like to earn at least $1,810 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

?		33,000
?		1,810
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?

What is the minimum total risk index?