Your friend's portfolio manager has suggested two energy...

Your friend's portfolio manager has suggested two energy stocks: Exxon Mobil (XOM) and British Petroleum (BP). XOM shares cost $\$ 80$ and yield $2 \%$ in dividends. BP shares cost $\$ 50$ and yield $7 \%$ in dividends. ${ }^{8}$ Your friend has up to $\$ 40,000$ to invest, and would like to earn at least $\$ 1,400$ in dividends. Draw the feasible region that shows how many shares in each company she can buy. Find the corner points of the region. (Round each coordinate to the nearest whole number.)

Key Concepts

Feasible Region

The feasible region, in the context of linear programming, is the set of all points that satisfy the given constraints. It typically takes the form of a convex polygon (in two dimensions) where every point within the region represents a potential solution that meets all budgetary and requirement conditions.

Corner Points

Corner points, also known as vertices, are the intersections of the boundaries that define the feasible region. These points are important because, when optimizing a linear objective function, an optimal solution—whether maximum or minimum—is always found at one of these vertices.

Linear Constraints

Linear constraints are equations or inequalities that limit the values of the decision variables. They represent the restrictions of the problem, such as budget limits or minimum dividend requirements, and together, they define the boundaries of the feasible region.

Dividend Yield

Dividend yield is the annual dividend payment expressed as a percentage of the stock's current price. This concept is used to estimate the income return on an investment, which directly influences the constraints based on minimum desired dividend income.

Investment Budget Constraints

Investment budget constraints refer to the limitations imposed by the available funds for investment. These constraints ensure that the total cost of purchasing any combination of assets does not exceed the investor's budget, thereby defining one of the key boundaries of the feasible region.

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