I would really appreciate if someone would actually solve this for me and see if my answer is correct. Thanks!

Find the minimum value of the expression C = 2x + 3y, where x and y are subject to the constraints

3y+4x=18
3y+x=9
x-1=0
y=0

I got 12?

Question

I would really appreciate if someone would actually solve this for me and see if my answer is correct. Thanks! 

Find the minimum value of the expression C = 2x + 3y, where x and y are subject to the constraints 

3y+4x>=18
3y+x>=9
x-1>=0
y>=0

I got 12?

anonymous · Answer

you still need help in this?

anonymous · Answer

Yes :) I just need the answer though because I have already solved and just want to see if my answer is correct.

anonymous · Answer

I got the same answer. I multiplied eq. 2 by -1 and add in eq.1. So I got x >= 3 and y >= 2. As we want the minimum, we plug in x = 3 and y = 2 and get C = 12.

anonymous · Answer

That is, both x >= 3 and y >= 2 satisfy the other 2 constrains, so we are okay doing it.

anonymous · Answer

Did you graph?

anonymous · Answer

Nope, solved the system analitically.

anonymous · Answer

Cool :) You can do it without graphing?

anonymous · Answer

http://www.quickmath.com/webMathematica3/quickmath/graphs/inequalities/advanced.jsp#c=plot_advancedgraphinequalities&v1=3*y%2B4*x+%3E%3D+18&v2=3*y%2Bx+%3E%3D+9&v3=x-1+%3E%3D+0&v4=y+%3E%3D+0&v7=x&v8=y&v9=0&v10=15&v11=0&v12=15 Here is the intersection of the solutions to the inequalities. Minimum is point (3,2)

anonymous · Answer

Nice! Thanks a lot for your help =)

anonymous · Answer

No problem, mate :-)