Problema Solution
Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $14,000/day to operate, and it yields 50 oz of gold and 3000 oz of silver each of x day. The Horseshoe Mine costs $16,000/day to operate, and it yields 75 oz of gold and 1000 oz of silver each of y day. Company management has set a target of at least 650 oz of gold and 18,000 oz of silver. How many days should each mine be operated so that the target can be met at a minimum cost?
Answer provided by our tutors
The conditions on x and y are:
x >= 0
y >= 0
50x+75y>= 650
3x+y >= 18 (in units of 1000 ounces)
The objective function is C(x, y) = 14x + 16y in thousand dollars.
We need to find the minimum for the objective function.
First we find the corner points of the graph :
The corner points are (13, 0), (0, 18) and (4, 6).
C(13, 0) = 14*13 + 16*0 = 182
C(0, 18) = 14*0 + 16*18 = 288
C(4, 6) = 14*4 + 16*6 = 152
Since 152 is the smallest value we conclude that the Saddle mine should operate 4 days and Horseshoe Mine should operate 6 days to minimize the cost.