Question

Graph the system of constraints. Name all vertices. Then find the value of x and y that maximize or minimize the objective function. Find the maximum or minimum value.
3x+y<_7
x+2<_9
x>_0, y>_0
Maximum for P= 2x+y

Answer 1

$$
3x+y <7\implies y < 7-3x\\
x+2<9\implies x < 7\\
x>0,y>0\implies\text{ Range and Domain is in Quadrant I}\\
\therefore 0<y<7-3x\text{ & } 0<x<7
$$
http://www.wolframalpha.com/input/?i=0%3Cy%3C7-3x%2C+0%3Cx%3C7

The vertices are easily found:

1) \(x=7\) and \(y=0\)
2)\(x=0\) and \(y=\cfrac{7}{3}\)
3) \(x=0\) and \(y=0\)

Using these three vertices, plug in to : \(P=2x+y\) and determine which of these <x,y> pairs makes P the largest.

Answer 2

*The vertices are easily found:
$$
1) ~x=\cfrac{7}{3},y=0\\
2) ~x=0,y=0\\
3) ~x=0,y=7
$$

Answer 3

is this the answer?

Answer 4

The answer is 1, 2 or 3 above. Plug in <x,y> into 2x+y for each and select the <x,y> that makes P the largest. For example, for 1): x=7/3,y=0, so P=2x+y=2(7/3)+0=14/3. This is P at <7/3,0>. Next, find P at <0,0> and at <0,7> and compare to P at <7/3,0>, which we just found to be 14/3.

Answer 5

BTW the <_ is actually