# 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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