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)?हल-क्षेत्र \(x\geq 0\), \(y\geq 0\), \(x+2y\leq 10\), \(3x+y\leq 12\) में (3x+2y) का अधिकतम मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (16)(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.कोनों पर जांचने से ((0,5)) पर (10), ((4,0)) पर (12), और \(\left(\frac{14}{5},\frac{18}{5}\right)\) पर (16) मिलता है। रैखिक व्यंजक का अधिकतम कोनों पर मिलता है।
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