# simplex method maximize objective function

• Feb 4th 2008, 08:46 AM
BenDunn
simplex method maximize objective function
A farmer has 100 acres to plant in corn and beans. Let c represent the # of acres planted in corn and b = # of acres planted in beans. It costs $72 / acre to plant corn and$40 / acre to plant beans. If the farmer has $12,000 to spend planting crops, how many acres should he plant in each crop if corn has a profit of$24 / acre and beans $32 / acre? Write the objective function and the system of constraints. Show the initial tableau and solve. My thoughts... I guess we are trying to get maximum revenue. It seems to me since beans are cheaper to plant and have higher profit, that we are going to plant all beans. Objective function: z = 32b + 24c (this seems like the amount of revenue?) Constraints ? b + c <= 100 40b + 72c <= 12000 Intial Tableau Can anyone give me any feedback as to whether I am on the right track? • Feb 4th 2008, 08:36 PM CaptainBlack Quote: Originally Posted by BenDunn A farmer has 100 acres to plant in corn and beans. Let c represent the # of acres planted in corn and b = # of acres planted in beans. It costs$72 / acre to plant corn and $40 / acre to plant beans. If the farmer has$12,000 to spend planting crops, how many acres should he plant in each crop if corn has a profit of $24 / acre and beans$32 / acre?

Write the objective function and the system of constraints.

Show the initial tableau and solve.

My thoughts... I guess we are trying to get maximum revenue. It seems to me since beans are cheaper to plant and have higher profit, that we are going to plant all beans.

Objective function: z = 32b + 24c (this seems like the amount of revenue?)

Constraints ? b + c <= 100

40b + 72c <= 12000

Intial Tableau

Can anyone give me any feedback as to whether I am on the right track?

What you have is correct.

To get the initial tableau you introduce initial slack variables e, f so we have:

z - 32b - 24c = 0

b + c +e = 100

40b + 72c + f= 12000

Then the initial tableau in matrix form is:

$\left[
\begin{array}{ccccc}
1&-32&-24&0&0\\
0&1&1&1&0\\
0&40&72&0&1
\end{array}
\right]$
$
\left[ \begin{array}{c}
z\\b\\c\\e\\f
\end{array}
\right]
=
\left[ \begin{array}{c}
0\\100\\1200
\end{array}
\right]
$

RonL