Here's the question bank on all the general aptitude topics.
X and Y are two positive real numbers such that 2X + Y ? 6 and X + 2Y ? 8. For which of the following values of (X, Y) the function f(X, Y) = 3X + 6Y will give maximum value?
Explanation:The given two equations are: 2X + Y ? 6 and X + 2Y ? 82X + Y ? 62X + Y = 6Put X = 0, we get Y = 6Put Y = 0, we get X = 3Hence, plotting the below pointsX03Y60X + 2Y ? 8X + 2Y = 8Put X = 0, we get Y = 4Put Y = 0, we get X = 8Hence, plotting the below pointsX08Y40For the given equations, the graph is as shown below.By solving this two equations 2X + Y = 6 and X + 2Y = 8, we get, X = 4/3 and Y = 10/3From the above graph, the extreme points are: (0,0), (3, 0), (0, 4) and (4/3, 10/3)At (3, 0), f(X, Y) = 3(3) + 6(0) = 9At (0, 4), f(X, Y) = 3(0) + 6(4) = 24At (4/3, 10/3) = 3(4/3) + 6(10/3) = 24From the given options, (4/3, 10/3) gives maximum for the function f(X, Y).
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