Ocean water contains 0.9 ounces of gold per ton. Method A costs $550 per ton of water processed and will recover 90% of the metal. Method B costs $400 per ton of water processed and will recover 60% of the metal. The two methods require the same capital investment and are capable of producing the same amount of gold each day. If the extracted gold can be sold for $1,750 per ounce, which method should be recommended? The supply of ocean water is essentially unlimited. Hint: Work this problem on the basis of profit per ounce of gold extracted.

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