Formulate but do not solve the following exercise as a linear programming problem. Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $15,000/day to operate, and it yields 30 oz of gold and 3,000 oz of silver each day. The Horseshoe Mine costs $17,000/day to operate, and it yields 65 oz of gold and 1,000 oz of silver each day. Company management has set a target of at least 550 oz of gold and 17,000 oz of silver. How many days should each mine be operated so that the target can be met at a minimum cost?
A) Minimize: Subject to:
B) Minimize: Subject to:
C) Minimize: Subject to:
D) Minimize: Subject to:

Question

Formulate but do not solve the following exercise as a linear programming problem. Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $15,000/day to operate, and it yields 30 oz of gold and 3,000 oz of silver each day. The Horseshoe Mine costs $17,000/day to operate, and it yields 65 oz of gold and 1,000 oz of silver each day. Company management has set a target of at least 550 oz of gold and 17,000 oz of silver. How many days should each mine be operated so that the target can be met at a minimum cost?
A) Minimize: Subject to: 
B) Minimize: Subject to: 
C) Minimize: Subject to: 
D) Minimize: Subject to:

Quizplus · Accepted Answer

We want to minimize the cost of operating the mines while meeting the target production of gold and silver. Let x be the number of days the Saddle Mine is operated and y be the number of days the Horseshoe Mine is operated.

The objective function is to minimize the cost: 
Cost = 15000x + 17000y

The constraints are:
Gold production: 
30x + 65y ≥ 550

Silver production: 
3000x + 1000y ≥ 17000

Non-negativity: 
x, y ≥ 0

Therefore, the correct choice is B.

Formulate but Do Not Solve the Following Exercise as a Linear