# Math Help - Value with constraints

1. ## Value with constraints

I tried to graph this one but it is not coming out:

Find the maximum value of C=6x+5y on the region determined by the constraints:
{3x+2y>20
{2<x<8
{1<y<10

17
36
41
47

2. Hello, Mike!

I'm not getting any of their answer-choices either . . .

Find the maximum value of $C\:=\:6x+5y$ on the region

determined by the constraints: . $\begin{Bmatrix}3x+2y\:\geq\:20 \\
2 \leq x \leq 8 \\ 1 \leq y \leq 10\end{Bmatrix}$

Answers: . $(1)\;17\quad(2)\;36\quad(3)\;41\quad(4)\;47$
Code:
    \ |     |(2,10)                         |(8,10)
10* - - * - - - - - - - - - - - - - - - * -
| \   | : : : : : : : : : : : : : : : |
|   \ |: : : : : : : : : : : : : : : :|
|(2,7)* : : : : : : : : : : : : : : : |
|     | \: : : : : : : : : : : : : : :|
|     |   \ : : : : : : : : : : : : : |
|     |     \: : : : : : : : : : : : :|
|     |       \ : : : : : : : : : : : |
1+ - - | - - - - * - - - - - - - - - - * -
|     |      (6,1)\                   |(8,1)
|     |             \                 |
- + - - * - - - - - - - * - - - - - - - * - -
|     2                 \             8

The maximum is at $(8,10)\!:\;\;C\:=\:6(8) + 5(10)\:=\:98$

Is there a typo?
Did they ask for the minimum?

3. Originally Posted by mike1
I tried to graph this one but it is not coming out:

Find the maximum value of C=6x+5y on the region determined by the constraints:
{3x+2y>20
{2<x<8
{1<y<10

17
36
41
47
The attached diagram shows the feasible region defined by the constraints.

The maximum value of C is taken at one of the vertices of the feasible
region, so we need only compute C at each vertex and choose the largest
value.

Computing the value of the objective we find the maximum at the vertex
(8,10), where the objective is 98.

And the minimum is 41 at vertex (6,1)

RonL