The Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $$14,000/$day to operate, and it yields $50$ oz of gold and $3,000$ oz of silver per day. The Horseshoe Mine costs $$16,000/$day to operate, and it yields $75$ oz of gold and $1,000$ oz of silver per day. Company management has set a target of at least $650$ oz of gold and $18,000$ oz of silver.

You boss would like you to focus on the following five issues:

$1.$ How many days should each mine be operated so that the target can be met at a minimum cost?

$2.$ Find the range of values that the Saddle Mine's daily operating cost can assume without changing the optimal solution.

$3.$ Find the range of values that the requirement for gold and silver can assume.

$4.$ Find the shadow price for the requirement for gold and silver.