Answer:
Method A should be recommended, because it produces a profit of $61.73 more than Method B
Explanation:
To determine, the recommended, method, let us calculate the amount needed to extract 1 ounce of gold using each method, then subtract these from the selling price to get the profit when each method is used.
Method A:
Recovery rate of metal = 90% = 90/100 = 0.9
Hence for 1 ton of water processed, amount of gold that can be recovered
= 0.9 × 0.9 = 0.81 ounces of gold.
Therefore, to produce 1 ounce of gold, we will solve as follows:
0.81 ounce of gold = 1 ton of water
∴ 1 ounce of gold = 1/0.81 = 1.2345679 ounces of water
Next, we are told that 1 ton of water costs $550 to process
∴ 1.2345679 tons of water = 550 × 1.2345679 = $679.01
Therefore, for method A, the effective amount in dollars used to extract 1 ounce of gold = $679.01
Calculating net income from this method is as follows
profit per ounce = selling price per ounce - cost price per ounce
profit per ounce = 1,750 - 679.01 = $1,070.99
Method B:
recovery rate of metal = 60% = 60/100 = 0.6
Hence for 1 ton of water processed, amount of gold that can be recovered
= 0.6 × 0.9 = 0.54 ounces of gold.
Therefore, to produce 1 ounce of gold, we will solve as follows:
0.54 ounce of gold = 1 ton of water
∴ 1 ounce of gold = 1/0.54 = 1.8518519 ounces of water
Next, we are told that 1 ton of water costs $400 to process
∴ 1.8518519 tons of water = 400 × 1.2345679 = $740.7
Therefore, for method B, the effective amount in dollars used to extract 1 ounce of gold = $740.74
Calculating net income from this method is as follows
profit per ounce = selling price per ounce - cost price per ounce
profit per ounce = 1,750 - 740.74 = $1,009.26
Since the net income from method A ($1070.99) is more than the net income from method B ($1,009.25), method A is recommended
