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August 9th, 2014, 08:36 PM  #1 
Newbie Joined: Aug 2014 From: Brsibane Posts: 2 Thanks: 0  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. 
August 9th, 2014, 10:20 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, Ben Parker! I can get you started. Quote:
$\begin{array}{ccccc} & \text{apple} & \text{p'apple} & \text{orange} & \text{Profit} \\ \hline C(x) & 500 & 300 & 200 & \$0.90 \\ P(y) & 300 & 400 & 300 & \$1.20 \\ H(z) & 200 & 200 & 600 & \$1.50 \\ \hline \text{Total} & 5000L & 4000L & 3000L \\ \hline \end{array}$ 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: $\:P \;=\;0.90x + 1.20y + 1.50z$  
August 10th, 2014, 08:19 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,117 Thanks: 1003 
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 ! 

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