If two constraints do not intersect in the positive quadrant of the graph, then A. The problem is infeasible B. The solution is unbounded C. One of the constraints is redundant D. None of the above
Hint: Hint: Here, we will determine the answer of the given condition by the help of the assumptions (properties) taken of the linear programming.
Complete step by step answer:
We are given the condition that if two constraints do not intersect in the positive quadrant of the graph, then we need to determine the nature of the solution obtained. For this, we will recall the properties of linear programming. The number of constraints should be expressed in the quantitative terms and it must be non – negative. The relationship between the constraints and the objective functions should be linear. The linear (objective) function is to be optimized (reformed to a certain extent). Now we have the condition i. e., the constraints must be non – negative. This non – negativity condition is applied because a variable can not take negative value because it is impossible to get negative capital values for anything like land, labour, etc. Therefore, due to condition I, the feasible region can only exist in Quadrant I. Hence, we can say that the problem is infeasible.
Option(A) is correct.
Note:: In mathematics, the method of reforming the algebraic operations provided with some constraints. The constraints can be equalities or inequalities. We use this method to either maximize or minimize the value of the given function. It is used in mathematics (majorly) as well as in other branches such as statistics and economics.