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 $12,000/day to operate, and it yields 50 oz of gold and 3000 oz of silver each of x day. The Horseshoe Mine costs $15,000/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?

(x,y)=

What is the minimum cost?

Explanation / Answer

let saddle mine operated for x days, horse shoe mine operated for y days.

total operating cost= 12000x+15000y

total gold from saddle mine= 50x silver- 3000y

total gold form horseshoe mine=75y silver=1000y

total gold= 50x+75y. it should be <= 650

total silver=3000x+1000y it should be <= 18000

objective function

minimise 12000x+15000y

constraints-

50x+75y<=650

3000x+1000y<=18000 i.e. 3x+y<=18

x>=0, y>=0

solve the LP to get the answer.

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