Formulate but do not solve the following exercise as a linear programming proble

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 $14,000/day to operate, and it yields 45 oz of gold and 3000 oz of silver each of x days. The Horseshoe Mine costs $18,000/day to operate, and it yields 80 oz of gold and 1250 oz of silver each of y days. Company management has set a target of at least 600 oz of gold and 19,000 oz of silver. How many days should each mine be operated so that the target can be met at a minimum cost C in dollars? Minimize C = subject to the constraints gold silver x greaterthanorequalto 0 y greaterthanorequalto 0

Explanation / Answer

Let x,y be respectively the number of days for which the two mines Saddle and Horseshoe operate.

The conditions on x,y are: x 0,y 0,

Gold target: 45x+80y 600,

Silver target: 3000x+1250y 19000

Objective function: Minimize C = 14000x + 18000y

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