Linear Programming

posted by .

OKay My question is:
Two factories manufacture 3 different grades per paper. the company that owns the factories has contracts to supply at least 16 tons of low grade, 5 tons of medium grade, and at least 20 tons of high grade paper. It cost $1000 per day to operate the first factory and 2000 per day to operate the second. Factory 1 produces 8 tons of low grade, 1 ton of medium grade, and 2 tons of high grade paper in day's operation. Factory 2 produces 2 tons of low grade, 1 ton of medium grade and 7 tons of high grade per day. how many days should each factory be in operation in order to fill the most economically?

Also i have to assign variables to x and y and state a goal plus represent the goal with an equation
then i have to write inequalities that represent the restrictions of this problem in a chart. Then i have to grade the system of inequalities, shade the solution region, and use corner points to analyze data and find the solution. Finally I write my solution in a complete sentence.
Help?

  • Linear Programming -

    So the instructions seem to be clear. Do you have a problem, or where is the problem if there is any?

  • Linear Programming -

    It's just I'm stuck at picking out what i need and such.. Not very good with word problems..

  • Linear Programming -

    You can take the question and split it up into constraints and costs.

    Requirements:
    "supply at least 16 tons of low grade, 5 tons of medium grade, and at least 20 tons of high grade paper."
    So minimum quantities = (16,5,20)
    Supplied by Factory 1, F1 = (8,1,2)/$1000
    Supplied by F2 = (2,1,7)/$2000

    So the constraints are:
    8F1+2F2 ≥ 16
    F1+F2 ≥ 5
    2F1+7F2 ≥ 20
    F1 ≥ 0
    F2 ≥ 0

    Cost=1000F1+2000F2

    Your graph will have F1 in the x-axis, F2 in the y-axis. Plot the constraint equations, and shade the solution (feasible) region. Find the optimal solution.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math / linear programming

    Two factories manufacture 3 different grades of paper. The company that owns the factories has contracts to supply at least 16 tons of low grade, 5 tons of medium grade, and at least 20 tons of high grade paper. It costs $1000 per …
  2. Algebra 2 (Linear Programming)

    The Carbon coal company has 2 mines, a surface mine ad a deep mine. it costs $200 per day to operate the surface mine and $250 to operate the deep mine. Each mine produces a medium grade and a medium-hard grade coal, but in different …
  3. Linear Programming

    Riverside oil company in eastern Kentucky produces 3 different grades of gasoline. They are regular, premium, and supreme grades. Each barrel of regular grade sells for $77 while premium grade sells for $82 per barrel and supreme grade …
  4. Finite Mathematics

    I just need help with the set up of this problem, that's where I'm getting lost. A mining company operates two coal mines, M1 and M2. The company sells the coal to three purchasers: two steel mills P1 and P2, and a power generating …
  5. linear programming

    Exeter Mines produces iron ore at four different mines; however, the ores extracted at each mine are different in their iron content. Mine 1 produces magnetite ore, which has a 70% iron content; mine 2 produces limonite ore, which …
  6. linear programming

    Exeter Mines produces iron ore at four different mines; however, the ores extracted at each mine are different in their iron content. Mine 1 produces magnetite ore, which has a 70% iron content; mine 2 produces limonite ore, which …
  7. Management Science

    Riverside oil company in eastern Kentucky produces 3 different grades of gasoline. They are regular, premium, and supreme grades. Each barrel of regular grade sells for $82 while premium grade sells for $88 per barrel and supreme grade …
  8. Math

    An oil company owns two refineries. The daily production limits and operating costs for each refinery are given in the table below. An order is received for 1540 barrels of high-grade oil, 1650 barrels of medium-grade oil, and 2860 …
  9. Math

    A steel plant has two sources of ore, source A and source B. In order to keep the plant running, at least three tons of ore must be processed each day. Ore from source A costs $20 per ton to process, and ore from source B costs $10 …
  10. Social Studies

    How could the North's factories be considered an advantage?

More Similar Questions