Question

Corner points of the feasible region for an LPP are (0, 2) (3, 0) (6, 0), (6, 8) and (0, 5). Let F = 4x + 6y be the objective function. The minimum value of F occurs at

• A. (0, 2) only
• B. (3, 0) only
• C. the mid-point of the line segment joining the points (0, 2) and (3, 0) only
• D. any point on the line segment joining the points (0, 2) and (3, 0)

Answer 1

Answer: (D)

any point on the line segment joining the points (0, 2) and (3, 0)

Answer 2

As seen here, at (0,2) and (3,0) points the obtained value of the equation 4x+6y = 12, which will minimum values among all.

The task of obtaining the most efficient optimal (maximum or lowest) value of a linear function with several variables (referred to as the objective function) is known as a linear programming problem (or LPP). Some requirements for LLP include that the variables fulfill a set of linear inequalities (also known as linear constraints) and be non-negative. These variables are non-negative and are also referred to as choice variables. Manufacturing issues, dietary issues, and transportation issues are the three main categories of linear programming problems.

The number of problems that can be optimized with linear programming has no upper bound. The most prevalent sorts of issues on board examinations are these three:

1. Manufacturing Issues: In these issues, we maximize profit while utilizing the fewest resources possible.
2. Diet Problem: To lower the cost of production, we compute the quantity of different nutrients in a diet.
3. Transportation Problem: In these issues, we compute the timetable to identify the most expedient and affordable means of shipping a product.