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 per ton to process. Costs must be kept to no more than $80 per day. Moreover, Federal Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. If ore from source A yields 300 lbs of steel per ton, and ore from source B yields 400 lbs of steel per ton, how many tons of ore from each source should be processed each day to maximize the amount of steel produced?

A) 1 ton from source A, 2 tons from source B

B) 2 tons from source A, 4 tons from source B

C) 3 tons from source A, 0 tons from source B


D) 4 tons from source A, 0 tons from source B

Is it D?

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  1. Surely this is not the same yolanda ?
    anyway
    x = tons A
    y = tons B
    constraints:
    x+y >/= 3
    20 x + 10 y </= 80
    y </= 2x

    then maximize 300 x + 400 y

    sketch all the constraints in the first quadrant to find corners
    above line from (0,3) to (3,0)
    below line from (0.8 to (4,0)
    below line from (0,0) to (4,8) slope 2

    that slope 2 line hits the others at
    (1,2) and at (2,4)

    now what is 300 x + 400 y
    at (2,4)
    600 +1600 = 2200 I bet that wins
    try (4,0) --> 1200 loser
    etc
    so 2 from A and 4 from B

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  2. LOL, I never thought of not doing the problem but just trying all the answers :)
    It amounts to the same thing but quicker.

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  3. Yes it is the same Yolanda lol thank you so much ! I really appreciate it. :)

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  4. You are welcome :)

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