So, this is our system of first-order conditions of Kuhn-Tucker's type, and we start analyzing as always with NDCQ checking. NDCQ is checked on the boundary of the constraint set. We're dealing with the factors of production which take only non-negative values. As for the equation of the isoquant, this is a separate problem, how to draw it. Actually, if we solve for x_2 in terms of x_1, we get a rational function whose graph is a hyperbola. So, here, if I choose some y value, we get something similar to this. So, either the solution belongs to the isoquant, excluding the endpoints, or it can happen, can occur somewhere here or there. If the point belongs to the isoquant and at the same time it's internal solution, meaning that both factors are employed in positive amounts, then all we have to do, we need to find the gradient and the gradient looks like, never turn zero, of course. Or if I choose either this point to that point, doesn't matter, these points are symmetric. For instance, if I choose that point, the Jacobian matrix will be a two-by-two matrix that will form the first row, and here we have X_2 equals zero, the second row. Well, clearly the rank of J is two always, so NDCQ holds. Now, we proceed solving the system. As always, we start with step one. We assume firstly, that the constraint is still written here but we can restore it if we look at the expression within the brackets and convert this minus sign into an inequality signs. So, we are assuming that x_1 x_2, plus x_1 plus x_2 is strictly greater than y. That entails the zero value for Lambda. Now, if Lambda is zero, we go back. Well, these are fulfilled. If Lambda is zero, negative 100 is less than zero, negative one is also less than zero. But here, the complimentary slackness for positive values of x_1 and x_2, it immediately follows that x_1 should equal x_2 equals zero. So, the factors are not employed at all. Meaning that from here we derive, the output is zero, but the problem is being solved on the assumption that y is positive, so it doesn't work. That means that the minimization takes place on the isoquant somewhere. Now, let's consider the case then we have x_1 star, optimal bundle of factors, x_2 star, greater than zero. This system is being slightly reduced and it becomes this time, a system of equalities alone, minus a 100 plus Lambda. Now, if we take these negative numbers and move to the right side and divide left-hand sides by left-hand sides and the same for right hand sides, we get, right here, a system of two equations with two unknowns. That becomes, or we can solve for x_2. So, x_2 equals, and substitute into equation, then we have. Or, if I divide this quadratic equation by 100, then I get something more suitable for analysis. I have a square. We're interested only in a positive root. Clearly we're interested in the case when x_1 is strictly greater than zero, that will provide a condition on the output, y. It happens only then one plus y is strictly greater than 100, so these case is finished. So, we were looking for solutions that belong to the isoquant but they are not corner solutions in a solution. That happens for big outputs, y is greater than 99. So, what's left? We need to check the corner solutions, either this or that. Since the first factor is much more expensive than the second, because the prices differ 100 times, well, economic intuition tells us that x_2 will be bought instead of x_1, but we need to check that mathematically, rigorously.