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 $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?

Answer 1

Answer:

Operate mine 1 four 4 days and mine 2 during 6 days to obtain minimum cost for the desired output of 850 gold and 18,000 silver

Explanation:

We generate the equation system on excel:

(50g + 3000s) Q_1 --> output generated on Mine 1

(75g + 1,000s) Q_2 --> output generated on Mine 2

12,000 Q1 + 17,000 Q2 = cost of the mines

we do solver to minimize the days of each mine considering a desired output of 18,000 silver and 650 gold:

and get the following:

M1  4 days  output: (50g + 3000s) 4 = 200 g    12,000s

M2 6 days  output: (75g + 1,000s) 6 =  450g      6,000s

Cost: 12,000 x 4 + 17,000 x 6 = 150,000