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?
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
LOL, I never thought of not doing the problem but just trying all the answers :)
It amounts to the same thing but quicker.
Yes it is the same Yolanda lol thank you so much ! I really appreciate it. :)
You are welcome :)
To determine the answer, we need to optimize the amount of steel produced while ensuring the constraints are met. Let's go through the options to find the correct answer.
Option A) 1 ton from source A, 2 tons from source B:
Processing 1 ton from source A will yield 1 * 300 lbs = 300 lbs of steel.
Processing 2 tons from source B will yield 2 * 400 lbs = 800 lbs of steel.
Total steel produced = 300 lbs + 800 lbs = 1100 lbs of steel.
Option B) 2 tons from source A, 4 tons from source B:
Processing 2 tons from source A will yield 2 * 300 lbs = 600 lbs of steel.
Processing 4 tons from source B will yield 4 * 400 lbs = 1600 lbs of steel.
Total steel produced = 600 lbs + 1600 lbs = 2200 lbs of steel.
Option C) 3 tons from source A, 0 tons from source B:
Processing 3 tons from source A will yield 3 * 300 lbs = 900 lbs of steel.
Total steel produced = 900 lbs of steel.
Option D) 4 tons from source A, 0 tons from source B:
Processing 4 tons from source A will yield 4 * 300 lbs = 1200 lbs of steel.
Total steel produced = 1200 lbs of steel.
From the options, it is clear that Option B provides the maximum amount of steel produced, with 2200 lbs. Therefore, the correct answer is:
B) 2 tons from source A, 4 tons from source B.
So the answer is not D, it is B.