2 A mining company is extracting silver and gold from two mi

2. A mining company is extracting silver and gold from two mines A and B. It costs $15,000 a day to operate mine A and $19,000 a day to operate mine B. Mine A yields 65 oz. of gold and 6500 oz. of silver each day. Mine B yields 90 oz. of gold and 4500 oz.of silver each day. Management has set a target of at least 800 oz. of gold and 11,000 oz. of silver. How many days should each mine be operated so that the target can be met at minimum cost? (Set up the LP problem, but do not solve! Label the variables.) Please identify the objective function to optimized and the constraints.

Solution

Variables

Let\'s say the mine A is operated A days

and the mine B is operated B days

Constraints

1) gold requirement meet : 65A + 90 B >= 800

2) silver requirement meet : 6500A + 4500 B >= 11000

3) A and B are non-negative integers

Objective

Minimize cost = 15000A + 19000B