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  1. #1
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    Business Math

    1. A glass blower makes glass decanters and glass trays on a weekly basis. Work in progress cannot be carried over from week to week. Each item requires 1 pound of glass, and the glass blower has 15 pounds of glass available each week. A glass decanter requires 4 hours of labor, a glass tray requires 1 hour of labor, and the glass blower works 25 hours a week. The profit from a decanter is $50, and the profit from a tray is $10.

    a. Find the optimal production schedule for this situation.

    b. If the glass blower received an order for 5 trays that she could not refuse, what would be the optimal production schedule?

    c. What would be the penalty for this additional constraint?
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by darkdesign007 View Post
    1. A glass blower makes glass decanters and glass trays on a weekly basis. Work in progress cannot be carried over from week to week. Each item requires 1 pound of glass, and the glass blower has 15 pounds of glass available each week. A glass decanter requires 4 hours of labor, a glass tray requires 1 hour of labor, and the glass blower works 25 hours a week. The profit from a decanter is $50, and the profit from a tray is $10.

    a. Find the optimal production schedule for this situation.

    b. If the glass blower received an order for 5 trays that she could not refuse, what would be the optimal production schedule?

    c. What would be the penalty for this additional constraint?
    Business Math-graph.jpg

    The three verticies show where a max can occur.

    Checking near each one( they are not all integers)

    we get

    15 glass trays 0 decanters
    12 glass trays 3 decanters
    1 glass tray 6 decanters

    plugging each of these into the profit function gives

    P(g,d)=50d+10g
    P(15,0)=50(0)+10(15)=150
    P(12,3)=50(3)+10(12)=270
    P(1,6)=50(6)+10(1)=310

    So the most profit occus with 6 decanters and 1 glass tray.

    for b and the constraint that g \ge 5

    find your new vertices and repeat the same process.

    I hope this helps.

    Good luck
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