Diketahui :
Ditanya :
Nilai maksimum ![begin mathsize 14px style z equals 2 x plus 3 y end style](data:image/png;base64,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)
Jawab :
Cari titik pojok dan titik potong dari setiap pertidaksamaan garis.
Titik pojok pertidaksamaan
Titik potong sumbu x,
Titik potong sumbu y,
Titik pojok pertidaksamaan
Titik potong sumbu x,
Titik potong sumbu y,
![begin mathsize 14px style rightwards double arrow D left parenthesis 0 comma 8 right parenthesis end style](data:image/png;base64,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)
Eliminasi pertidaksamaan (1) dan pertidaksamaan (2)
Substitusi
ke persamaan (1)
Jadi, titik potong persamaan garis (1) dan (2) adalah :
![begin mathsize 14px style rightwards double arrow E left parenthesis 8 comma 4 right parenthesis end style](data:image/png;base64,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)
Dengan memperhatikan syarat
dan
, maka daerah arsiran grafik akan berada diatas sumbu-
, dan di sebelah kanan sumbu-
Tanda pertiaksamaan dari ke-2 sistem pertidaksamaan adalah
, maka arsiran nya akan berada dibawah garis .
Perhatikan grafik berikut :
Untuk mencari nilai maksimum, maka substitusikan semua titik yang berada pada daerah arsir, yaitu titik A,E dan D ke fungsi objektif ![begin mathsize 14px style z equals 2 x plus 3 y end style](data:image/png;base64,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)
![begin mathsize 14px style rightwards double arrow A left parenthesis 12 comma 0 right parenthesis end style](data:image/png;base64,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)
![begin mathsize 14px style rightwards double arrow E left parenthesis 8 comma 4 right parenthesis end style](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADsAAAAOCAYAAACRkmStAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAbFJREFUeNpjYBg4UAnE1TQ2v5JhEAA/IF5OB3uWQu2iGQgC4v84MMhyFiC+C8TCSHr4gLgPiF8C8S8g/gRVq0JC4P3HIg6y4xYQs5HqiTQi1dUDcQke+WQgnoQmthuIDYCYCcpngvJvEWGfIBBfw+FZBqhdyaR6tgea9AiF0ioCSWcNEPugib2GOhrdE8+JcNdiII7E41kfqJ1YwX8C+DAWhyEDUGxI4pEHJVUeNDEvID4JxMZQvjUQX4J6Ah/wgQYuAx7PckEDkywAit0tOORAye8PlgD6gaTmDw69JVC1r6F0PBHJ9xJS3v+PR+0vcmP2IJ6YNQfi/QQcic2z9tB8Zw6NdVMgng0VxwUWQgtDBko8iy/PriKQZ0HJbj4Bc55DS19kcAGIldDEOKABQGqkoAMeaNYhCRBTohFT8mEroH4hlcQwAKqivpHgPrIKKErAOiD2ICLQ0KueDUCch+RhFmjraiFaqbuGDM9OAeJEWnj2HZ7kBUv+bNASWxgtqU2CFk6gPP0UiDvQssxTaGODFM+KA/ENchoVg6G5eGmwNRdp1VAvIaI6Qga1QFyOLAAAMvx/V2x578YAAACtdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdHlsZSBtYXRoc2l6ZT0iMTRweCI+PG1vPiYjeDIxRDI7PC9tbz48bWk+RTwvbWk+PG1vPig8L21vPjxtbj44PC9tbj48bW8+LDwvbW8+PG1uPjQ8L21uPjxtbz4pPC9tbz48L21zdHlsZT48L21hdGg+49DWTgAAAABJRU5ErkJggg==)
Jadi, nilai maksimum adalah 28.