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30 October, 10:30

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.

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  1. 30 October, 10:55
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    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
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