A Linear Programming Problem Has Two Constraints 2X + 4Y

question 20

Multiple Choice

A linear programming problem has two constraints 2X + 4Y ≥ 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is true?

• A) There are four corner points including (50, 0) and (0, 12.5).
• B) The two corner points are (0, 0) and (50, 12.5).
• C) The graphical origin (0, 0) is in the feasible region.
• D) The feasible region is triangular in shape, bounded by (50, 0), (33-1/3, 8-1/3), and (100, 0).
• E) The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.

---

Definitions:

Taxpayer

An individual or entity that is obligated to make payments to governmental authorities based on income earned or goods and services provided.

Dependent Child

A dependent child is an individual, typically under the age of 19 (or 24 if a student), who is financially supported by a taxpayer and qualifies them to claim dependent-related tax benefits.

Wages

A fixed regular payment, typically calculated on an hourly, daily, or piecemeal basis, made by an employer to an employee, especially to a manual or unskilled worker.

Tax Liability

The total amount of tax owed by an individual, corporation, or other entity to a taxing authority, such as the IRS or state tax agency.