Linear Programming

The feasible region is a convex polygon. Evaluating z=4x+3y at all corner points of the feasible region, the minimum value obtained is: zᵢₙ=220

Let the width of the river be x. From first position: 60^=(h)/(x) h=√(3)x From second position: 30^=(h)/(x+20)=1√(3) h=x+20√(3) Equating values of h: √(3)x=x+20√(3) 3x=x+20 x=10 Thus breadth =10√(3) ft.

In right triangle: (a²-b²)/(a²+b²)=(A-B)

P(A ∩ B) = P(A)·P(B|A) = 1/4 · 2/3 = 1/6
P(A|B) = (P(A ∩ B)) / P(B) = 1/2 ⇒ P(B) = (1/6) / (1/2) = 1/3

The above question asks for the impact of change in constraints on the Linear programming problem. In this scenario, when there is a change in constraint, the solution will change definitely. Whether the solution exists or not, we can only find once the problem is re-evaluated.
In an LPP, the objective function is related to the main objective of any problem, either we have to maximize or minimize the function based on the situation whereas the constraints is related to physical restrictions in achieving the defined objective function. In real life problems, there might be situations when the constraints change, but objective function does not changes to accommodate the change in constraints. Thus, if constraints in linear programming problem is changed, the problem has to be re-evaluated for the same objective function and after solving we can find whether the solution exists or not.