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Question

Pearson's Metals mines two ores: R and S. The company extracts minerals A and B from each type of ore. It costs $50 per ton to extract 80 lb of A and 160 lb of B from ore R. It costs $60 per ton to extract 140 lb of A and 50 lb of B from ore S. Pearson's must produce at least 4000 lb of A and 3200 lb of B. How much of each ore should be processed to minimize cost? What is the maximum cost?

Answers
13.48 tons of ore R and 20.87 tons of ore S
$1926.20

Answer 1

Let x = the number of tons R
Then 80x = amount of A and 160 x = amount of B
Let y = number of tons of S
Then 140y amount of A and 50y = amount of B
80x+140y =4000
160x +50y =3200
-80x -25y = -1600
115y = 2400
y = 20.87 tons of S
160x +50(20.87) = 3200
160 x =3200 - 1043.5 = 2156.5
x = 13.48 tons of R
Total cost = 50(13.48)+60(20.87) = $1926.10