My Math Forum  

Go Back   My Math Forum > College Math Forum > Applied Math

Applied Math Applied Math Forum


Thanks Tree1Thanks
  • 1 Post By Joppy
Reply
 
LinkBack Thread Tools Display Modes
March 10th, 2016, 09:24 PM   #1
Newbie
 
Joined: Mar 2016
From: Milwaukee

Posts: 3
Thanks: 0

Linear Programming of Mixed Nut Assortment

Below is a problem on Linear Programming. I think I have a start to it, but I'm in a rut right now so I was wondering if I could receive a little help. Here's the problem

A candy store sells three different assortments of mixed nuts containing varying amounts of almonds, pecans, cashews, and walnuts. To preserve the store's reputation for quality, certain maximum and minimum percentages of the various nuts are required for each type of assortment, as shows in the following table.

Nut Assortment: Regular

Requirements: Not more than 20% cashews, not less than 40% walnuts, not more than 25% pecans, no restriction on almonds

Selling price per pound: $0.89

Nut Assortment: Deluxe

Requirements: Not more than 35% cashews, not less than 25% almonds, no restriction on walnuts and pecans

Selling price per pound: $1.10

Nut Assortment: Blue Ribbon

Requirements: Between 30% and 50% cashews, not less than 30% almonds, no restriction on walnuts and pecans

Selling price per pound: $1.80

Below is the cost per pound for each nut as well as the max quantity available per week

Almonds: $0.45/pound. 2000 lbs available per week

Pecans: $0.55/pound. 4000 lbs available per week

Almonds: $0.70/pound. 5000 lbs available per week

Almonds: $0.50/pound. 3000 lbs available per week

The store would like to determine the exact amounts of almonds, pecans, cashews, and walnuts that should go into each weekly assortment to maximize its weekly profit.

Here's what I have so far:

X1 = The assortment of cashews in the regular mix in pounds

X2 = The assortment of walnuts in the regular mix in pounds

X3 = The assortment of pecans in the regular mix in pounds

X4 = The assortment of almonds in the regular mix in pounds

X5 = The assortment of cashews in the deluxe mix in pounds

X6 = The assortment of almonds in the deluxe mix in pounds

X7 = The assortment of walnuts in the deluxe mix in pounds

X8 = The assortment of pecans in the deluxe mix in pounds

X9 = The assortment of cashews in the blue ribbon mix in pounds

X10 = The assortment of almonds in the blue ribbon mix in pounds

X11 = The assortment of walnuts in the blue ribbon mix in pounds

X12 = The assortment of pecans in the blue ribbon mix in pounds

Cost Constraints (obtained from multiplying cost per pound by max quantity)

0.45(X4+X6+X10) ≤ $900 per week

0.55(X3+X8+X12) ≤ $2200 per week

0.7(X1+X5+X9) ≤ $3500 per week

0.5(X2+X7+X11) ≤ $1500 per week

Objective Function

This is where I need some help now after thinking about this problem. I can't figure out how to tie in the selling price per pound with the cost per pound for each specific nut. Could anyone provide some clarification? Many thanks.

Last edited by maxmatt20; March 10th, 2016 at 09:27 PM.
maxmatt20 is offline  
 
March 10th, 2016, 09:28 PM   #2
Newbie
 
Joined: Mar 2016
From: Milwaukee

Posts: 3
Thanks: 0

The formatting seems to be extremely skewed, but weirdly enough works very rarely. Please let me know if this is an issue for anyone else who is viewing this
maxmatt20 is offline  
March 10th, 2016, 09:29 PM   #3
Senior Member
 
Joined: Feb 2016
From: Australia

Posts: 1,737
Thanks: 606

Math Focus: Yet to find out.
Funny. This was an assignment in my highschool math class... I probably still have the full written report.
Thanks from maxmatt20
Joppy is offline  
March 10th, 2016, 09:35 PM   #4
Newbie
 
Joined: Mar 2016
From: Milwaukee

Posts: 3
Thanks: 0

@Joppy That would be of tremendous, tremendous help
maxmatt20 is offline  
Reply

  My Math Forum > College Math Forum > Applied Math

Tags
assortment, linear, mixed, nut, programming



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Linear programming Mathprog Math Software 0 December 6th, 2014 12:05 AM
Linear programming mathmaniac Algebra 10 February 19th, 2013 07:19 PM
Linear programming help TheFool89 Linear Algebra 0 August 23rd, 2010 03:24 AM
Linear Programming Help anarchy404 Algebra 8 November 18th, 2009 12:18 AM
Linear Programming maria69 Algebra 2 February 18th, 2009 11:12 AM





Copyright © 2018 My Math Forum. All rights reserved.