formulate but do not solve the following exercise as a linear - programming problem.\nperth mining company…

formulate but do not solve the following exercise as a linear - programming problem.\nperth mining company operates two mines for the purpose of extracting gold and silver. the saddle mine costs $16,000/day to operate, and it yields 60 oz. of gold and 300 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 750 oz of gold and 18,000 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?\nminimize c = \nsubject to the constraints\ngold\n\nsilver\n\nx≥0\ny≥0\nresources\nebook

formulate but do not solve the following exercise as a linear - programming problem.\nperth mining company operates two mines for the purpose of extracting gold and silver. the saddle mine costs $16,000/day to operate, and it yields 60 oz. of gold and 300 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 750 oz of gold and 18,000 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?\nminimize c = \nsubject to the constraints\ngold\n\nsilver\n\nx≥0\ny≥0\nresources\nebook

Answer

Explanation:

Step1: Define the cost function

The Saddle Mine costs $16000 per day and operates for $x$ days, and the Horseshoe Mine costs $18000 per day and operates for $y$ days. So the cost function $C$ to be minimized is $C = 16000x+18000y$.

Step2: Define the gold - constraint

The Saddle Mine yields 60 oz of gold per day and the Horseshoe Mine yields 80 oz of gold per day. The company wants at least 750 oz of gold. So the gold - constraint is $60x + 80y\geq750$.

Step3: Define the silver - constraint

The Saddle Mine yields 300 oz of silver per day and the Horseshoe Mine yields 1250 oz of silver per day. The company wants at least 18000 oz of silver. So the silver - constraint is $300x+1250y\geq18000$.

Answer:

Minimize $C = 16000x + 18000y$ subject to the constraints: Gold: $60x+80y\geq750$ Silver: $300x + 1250y\geq18000$ $x\geq0$ $y\geq0$