Question

Iron ore is a material extracted from a mine. besides iron it contains other impurities. once the ore is extracted, it is purified to obtain pure iron. the company "iron crew" decides whether to launch a new mine and is conducting ore analysis. you are an analyst hired to help company make a decision. read the data below and then answer the questions. the extracted 12-ton sample contained 4.8 tons of pure iron. the mine plans to extract a daily quantity of up to 2000 tons of ore. the cost of extraction and purification is estimated to be 54 dollars per ton of ore. the market price of a ton of pure iron is 120 dollars. does it make sense to open the mine? at what minimum percentage of iron content in the ore would the mine break even?

a) Yes; 45%

b) No; 32%

c) Yes; 60%

d) No; 25%

Answer 1

To determine if it makes sense to open the mine, we need to consider the potential profit. The mine would break even when the ore has a minimum percentage of iron content of 45%.

Step-by-step explanation:

To determine if it makes sense to open the mine, we need to consider the potential profit. The company would earn money by selling the pure iron extracted from the ore. The cost of extraction and purification is estimated to be $54 per ton of ore, while the market price of a ton of pure iron is $120. The 12-ton sample contained 4.8 tons of pure iron, so the profit from that sample would be (4.8 * 120) - (12 * 54) = $576.

To break even, the company needs to cover the costs of extraction and purification. This means the profit should be zero. Let x be the percentage of iron content in the ore. The profit from the 12-ton sample can be expressed as (x/100 * 12 * 120) - (12 * 54). Setting the profit equation to zero, we can solve for x:

x/100 * 12 * 120 - 12 * 54 = 0

x * 12 * 120 - 12 * 54 * 100 = 0

x = (12 * 54 * 100) / (12 * 120) = 45%

Therefore, the mine would break even when the ore has a minimum percentage of iron content of 45%.