## Related questions with answers

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 $50 \mathrm{oz}$ of gold and $3000 \mathrm{oz}$ of silver per day. The Horseshoe Mine costs $\$ 16,000 /$ day to operate, and it yields $75 \mathrm{oz}$ of gold and 1000 ounces of silver per day. Company management has set a target of at least $650 \mathrm{oz}$ of gold and 18,000 oz of silver.

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

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

c. Find the range of values that the requirement for gold can assume.

d. Find the shadow price for the requirement for gold.

Solution

Verified#### a.

This linear programming problem was solved as an exercise in the set of section 3.3.

The linear programming problem to solve is:

Minimize $C=14,000x+16,000y$

subject to

$\left\{\begin{array}{lll} 50x & +75y & \geq 650\\ 3000x & +1000y & \geq 18,000 \end{array}\right.$

and $x\geq 0,\ y\geq 0.$

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(See comment section below the solution for the link)

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