Perth Mining Company operates two mines for the purpose of extracting gold and s

Question

Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $16,000/day to operate, and it yields 50 oz of gold and 3000 oz of silver each of x day. The Horseshoe Mine costs $17,000/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?

What is the minimum cost?
$

Explanation / Answer

Saddle Mine = x days

Horseshoe Mine= y days

Minimize

C(x)=16000x +17000y

if

50x+75y>=650

and

3000x+1000y>=18000

Thus,

The minimum value is at (x,y)=(4,6) and minimum cost is $166000

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