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In the solution region \(x\geq 0\), \(y\geq 0\), \(x+2y\leq 10\), and \(3x+y\leq 12\), what is the maximum value of (3x+2y)?

Answer and explanation

Correct answer: (16)

Checking the corners gives (10) at ((0,5)), (12) at ((4,0)), and (16) at \(\left(\frac{14}{5},\frac{18}{5}\right)\). A linear expression attains its maximum at a corner.

Related tags

Linear InequalitiesMaximum ValueCorner MethodObjective FunctionGraphical Solution Of Linear Inequalities In Two VariablesMathematicsClass 11 Mcq

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