 Hello and how will you work today? The question says, David wants to invest at most Rs 12,000 in bond A and B. According to the rule, he has to invest at least Rs 2,000 in bond A and at least Rs 4,000 in bond B. If the rate of interest on bond A and B respectively are 8% and 10% per annum, formulate the problem of LPP and solve it graphically for maximum interest. Also determine the maximum interest received in a year. So here, let David invest in bond A, B is Y in bond, then the interest in bond A is 8% that means 8% in bond A plus in bond B total interest income, right? And we need to, this interest takes upon 100 plus Y or on simplifying, we can write it as Z as interest. So given some constraint to it, given that X should be at least 2,000, Y should be at least 4,000, crazy inequalities that we have are, X should be greater than equal to 2,000, Y should be greater than equal to 4,000 and the sum should be less than equal to 12,000. Let's first find out from here, 0 we have the value of Y as, or let's take, take the value of 4,000, we have the value of Y as 8,000, we have the value of X also as 6,000. So let us plot these three lines on a graph. This is a required presenting the equation X is equal to 2,000, this is the line representing the equation Y is equal to 4,000 and this is the line representing the equation X plus Y is equal to 12,000. This shaded region portion that is satisfying all these inequalities. The coordinates of this point are coming out to be 1,000. If we extend this Y line, whose coordinates are corresponding value of out to be 1, 1, 2, 0. So obviously Z is maximum amount 10. I hope you understood this graph.