Problem $5(10$ pts$).$ Solve the following problem using branch and bound.

$mamize,3x+10y+13z$

subject $to2y+3z5$

$,x+y+2z4$

$,x+2y+3z7$

$,x,y,z0$

$,x,y,z$ integers

This will require using the simplex algorithm a couple of times. You can do this by hand, or you

can use the simplex algorithm code from this course to help you $($including the two$-$phase algorithm

code if you wrote it in Homework $4).$ If you use code, include your code, how you use it$,$ and the

output. Please do NOT print individual steps in the simplex algorithm, as optimal dictionaries for

individual problems $($including Phase I problems when appropriate$)$ are sufficient for understanding

your work.