Math

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The Oscar Drapery Company makes three types of draperies at two different locations. At location 1, it can make 10 pairs of deluxe draperies, 20 pairs of better draperies, and 13 pairs of standard drapes per day. At location 2, it can make 20 pairs of deluxe drapes, 50 pairs of better, and 6 pairs of standard per day. The company has orders for 2000 pairs of deluxe drapes, 4200 pairs of better drapes, and 1200 pairs of standard drapes. If the daily costs are $500 per day at location 1 and $800 per day at location 2, how many days should Oscar schedule at each location in order to fill the orders at minimum cost? Find the minimum cost.

  • Linear programming -

    x = days at Loc 1
    y = days at Loc 2
    then limits and intecepts
    deluxe 10x+20y >/= 2000 (0,100)(200,0)
    better 20x+50y >/= 4200 (0,84)(210,0)
    standard 13x+6y >/= 1200 (0,200)(92.3,0)
    graph those
    and cost constraint c = 500 x + 800 y
    Now test upper corners
    try (0,200) all loc 2
    c = 800(200) = 160,000
    try (210,0) all loc 1
    c = 500(210) = 105,000 better
    Try also the intersection of the other lines to see if you get a lower cost solution

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