Youareprovidedwiththefollowingintegerprogram:

minz= 3x ys.t.

x+y 10xy1.5x+3y 5x9.5

y3.5

x,y0andinteger

1. Onthefollowing page,usethegraphicalsolution methodtoidentify thefeasiblepoints. (Use the scale 1 by 1 for each small square so that you can visuallydetectthefeasible integersolutions.)
2. Findtheextremepoints oftheconvexhullandcalculatetheirobjectivevalues.

Extremepoint1:

Extremepoint2:

Extremepoint3:

Extremepoint4:

Extremepoint5:

Extremepoint6:

1. Draw an isoprofit line that passes through the point (x=5, y=0) and find thedirectionofoptimization.
2. Providetheoptimalsolutionandoptimalobjective functionvalue.

Optimalsolution:x= y=

Optimalobjectivevalue: