# Value with constraints

• Jan 23rd 2007, 02:12 AM
mike1
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
• Jan 23rd 2007, 04:37 AM
Soroban
Hello, Mike!

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

Quote:

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

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

Answers: .$\displaystyle (1)\;17\quad(2)\;36\quad(3)\;41\quad(4)\;47$

Code:

    \ |    |(2,10)                        |(8,10)     10* - - * - - - - - - - - - - - - - - - * -       | \  | : : : : : : : : : : : : : : : |       |  \ |: : : : : : : : : : : : : : : :|       |(2,7)* : : : : : : : : : : : : : : : |       |    | \: : : : : : : : : : : : : : :|       |    |  \ : : : : : : : : : : : : : |       |    |    \: : : : : : : : : : : : :|       |    |      \ : : : : : : : : : : : |     1+ - - | - - - - * - - - - - - - - - - * -       |    |      (6,1)\                  |(8,1)       |    |            \                |     - + - - * - - - - - - - * - - - - - - - * - -       |    2                \            8

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

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

• Jan 23rd 2007, 04:52 AM
CaptainBlack
Quote:

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