My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
August 9th, 2014, 08:36 PM   #1
Newbie
 
Joined: Aug 2014
From: Brsibane

Posts: 2
Thanks: 0

Question Yr11 math C Assignment

Hey guys, I have a really hard question from my assignment; wondering if anyone could take a look and help me.

Question:
Simplex Algorithm

A fruit drink company makes three types of punch. C punch contains 500ml of apple/pear juice, 300ml of pineapple juice and 200ml of orange juice per litre. P punch contains 300ml of apple and peer juice, 400ml of pineapple juice and 300ml of orange juice per litre. H punch contains 200ml of apple/pear juice, 200ml of pineapple juice and 600ml of orange juice per litre.

the company makes profit \$0.90 per litre on C, \$1.20 per litre on P and \$1.50 per litre on H. At present the company has limited supplies: 5000L of pear and pineapple, 4000L of pineapple and 3000L of orange juice.

Define and Determine:
a. the decision variables
b. the three constraint in equations based on limited supply of the tree different juices
c. the profit function
d. the complete simplex tableau to be used to determine maximum profit
e. the amount of each type of punch to be produced to achieve maximum profit
f. the amount of each type of juice to be produced to achieve maximum profit
g. the maximum profit

If anyone can help it would be great,

Thanks Ben

Last edited by skipjack; August 11th, 2014 at 03:02 PM.
Ben Parker is offline  
 
August 9th, 2014, 10:20 PM   #2
Math Team
 
Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 407

Hello, Ben Parker!

I can get you started.


Quote:
A fruit drink company makes three types of punch.
C punch contains 500ml of apple juice, 300ml of pineapple juice and 200ml of orange juice per litre.
P punch contains 300ml of apple juice, 400ml of pineapple juice and 300ml of orange juice per litre.
H punch contains 200ml of apple juice, 200ml of pineapple juice and 600ml of orange juice per litre.

The company makes profit \$0.90 per litre on C, \$1.20 per litre on P and \$1.50 per litre on H.
At present the company has limited supplies: 5000L of apple, 4000L of pineapple and 3000L of orange juice.

$\begin{array}{c|c|c|c|c|}
& \text{apple} & \text{p'apple} & \text{orange} & \text{Profit} \\ \hline
C(x) & 500 & 300 & 200 & \$0.90 \\
P(y) & 300 & 400 & 300 & \$1.20 \\
H(z) & 200 & 200 & 600 & \$1.50 \\ \hline
\text{Total} & 5000L & 4000L & 3000L \\ \hline \end{array}$

Constraints:$\;\;\; \begin{Bmatrix}
500x + 300y + 200z & \le & 5,\!000,\!000 \\
300x + 400y + 200z & \le & 4,\!000,\!000 \\
200x + 300y + 600z & \le & 3,\!000,\!000 \end{Bmatrix}$

Profit: $\:P \;=\;0.90x + 1.20y + 1.50z$

soroban is offline  
August 10th, 2014, 08:19 PM   #3
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 12,752
Thanks: 860

2 solutions:
10,000 bottles of P punch
4000 bottles of C punch and 7000 bottles of P punch

Both bring in $12,000

Nobody gets to drink H punch !
Denis is online now  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
assignemnt, assignment, math, yr11



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
A Level Math resources (Edexcel modular math textbooks) Sid Math Books 5 May 27th, 2014 12:20 PM
Iphone math game? Speed math monkey chuckycheese Elementary Math 1 May 22nd, 2014 03:45 AM
A Level Math resources (Edexcel Modular Math textbooks) Sid Academic Guidance 2 May 11th, 2014 07:23 AM
A book on basic math that explains how math really works mishaark Math Books 6 September 8th, 2012 06:19 AM
A book on basic math that explains how math really works mishaark Elementary Math 0 December 31st, 1969 04:00 PM





Copyright © 2018 My Math Forum. All rights reserved.