Results 1 to 4 of 4

Math Help - Help with Factory Planning Problem

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    3

    Help with Factory Planning Problem

    Hi everyone!

    I wonder if someone could help with this. I am new to this site, so I am not quite sure whether I am posting it in correct field.

    In planning their production of two products, X and Y, a company has to take into account the demand for these products, as well as their internal production capacity. In addition they can (if necessary) buy in these products from a third party supplier.
    For the forthcoming month demand is estimated to be 120 units for X and 150 units for Y. The company sells these products for 25 and 34 for X and Y respectively. The company can buy X from its third party supplier for 20 per unit, and Y for 24 per unit.
    These products are produced on a single machine in the company. This machine costs 3 per hour to run when making X or Y and there are 175 working hours available in the forthcoming month on this machine for the production of X or Y. Producing one unit of X on the machine requires 4.5 hours, producing one unit of Y requires 6.5 hours. Technological constraints mean that the ratio of the number of units of Y produced on the machine to the number of units of X produced on the machine must be at least 1.3.
    By formulating and solving an appropriate linear program determine (for the forthcoming month) how much of each product should be made and how much should be bought from the third party supplier.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    Calculate how much profit you make by producing and selling one unit of X, and calculate the same for Y. Also calculate how much profit you make by buying one unit of X from your third-party supplier and selling it, and calculate the same for Y. Since you are going to make a profit on any of these actions, you should try to meet the demand for both X and Y through some combination of these actions, but you have to prioritize based on what makes you the most money. I would suggest writing a function of total profit in terms of p and q, where p is the number of units of X produced, and q is the number of units of Y produced. Then 120 - p should be the number of units of X purchased from the third party supplier and 150 - q should be the number of units of Y purchased from the third party supplier. Then maximize the function.

    Constraints are:

    4.5p + 6.5q \leq 175

    \frac{q}{p} \geq 1.3
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2010
    Posts
    3
    Thanks a lot for this.

    I calculated it as follows:

    profit for X produced is GBP 25 -(3 x 4.5)=11.5
    Profit for Y produced is GBP 34-(3x6.5)=14.5

    thus

    maximise11.5x +14.5y

    Constraints
    1.3y-x=0
    4.5x+6.5y=175


    iso-profit 11.5x +14.5y=180

    feasible region is at the vertex of the above curves

    so

    x=1.3y

    4.5 (1.3y) + 6.5y =175
    5.85y + 6.5y=175
    12.35y=175
    y=14.17 (to two decimal points)
    x = 18.42 (to two decimal points)


    so X bought = 120-14 = 106
    Y bought = 150-18=132


    but I am sure that I am wrong somewhere as I did not use buying cost of X and Y


    I thought to calculate total profit of X as 11.5 (produced)+ 5 (bought)=16.5
    Y 14.5 (produced) and 10 (bought)= 24.5

    and rewrite

    maximise
    16.5x+24.5 y

    but I am not sure... totally lost
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Mar 2010
    Posts
    3

    More help needed on this matter

    Does anyone else have any suggestions/ideas on this matter, please?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Max's Bells in a Factory
    Posted in the Math Puzzles Forum
    Replies: 0
    Last Post: May 8th 2010, 04:17 AM
  2. Multi-Agent Path Planning Optimization Problem.
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 14th 2010, 04:08 AM
  3. Linear Programming - Investment Planning Problem
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 20th 2009, 01:37 PM
  4. Financial Planning
    Posted in the Math Topics Forum
    Replies: 6
    Last Post: January 11th 2007, 03:51 AM

Search Tags


/mathhelpforum @mathhelpforum