LPs are used to find an optimal point but in some cases the feasible region is not bounded and extends upto infinity. How such anomaly occurs, knowing the cases for which LPs are used such as production problem, allocation problem, variables cannot reach upto infinite because that would only make the objective function reach positive or negative infinity?
True that no variable can reach infinite in real world and generally this arises as a result of incorrect formulation, some constraints are not taken care of, for ex. x>=0, y>=0. For ex: In a production problem the above mentioned condition is to be taken care of. Also, it can be a result of user's error, if the LP is solved in opposite sense, like solving a minimisation LP with maximisation sense.
Laying the foundation of calculus are two terms, differentiation and integration. The formula application of these two doesn't really explain the concept intuitively. What does these terms intuitively mean?
Differentiation: By differentiation, we mean dividing, dividing into infinitely small parts. And owing to the method and size of division, the domain of differentiation is much larger as compared to that of normal/perceivable division. Integration: By integration, we mean adding, addition of infinitely small parts. And any process/path could be made up by adding infinitely small pieces. The applications of these two processes are infinite; such as in aeronautics, to derive maximum and minimum value in real life scenarios,
Explain the concept of Substitution effect and Income effect with examples from real situation?
Suppose a consumer buys Pepsi and Pizza and the price of Pepsi has fallen down. Now that the price of Pepsi has fallen, I get more Pepsi for every Pizza that I give up. Because Pizza is now relatively more expensive, I should buy less Pizza and more Pepsi (Substitution Effect, change in consumption on the same Indifference Curve with a different MRS ). Now that Pepsi is cheaper, my income has greater purchasing power. I am, in effect, richer than I was. Because I am richer, I can buy both more Pizza and more Pepsi (Income Effect, change in consumption that results from the movement to a higher IC). Hence, both the effects affect the consumer's preferences in different ways.