The total cost for Company X to produce a batch of tools is

The problem first asks us to calculate the gross profit. The profit equation is as follows:

Profit = Revenue – Cost

In this particular case, we are given VARIABLE REVENUE and VARIABLE COST. This means that Company X makes a certain amount of revenue PER TOOL and has a certain cost PER TOOL. We also are given a FIXED COST. This is a cost that is constant and will not change. Thus we need to take into account the quantity of tools being produced and sold as well as the fixed cost. We can now generate a more detailed profit equation:

Profit = (number of tools sold)(revenue per tool) – [fixed cost + (number of tools made)(cost per tool)]

We are given the following:

fixed cost = $10,000

cost per tool = $3

revenue per tool = $8

Number of tools produced and sold = 20,000

We can now plug all this into our profit equation:

Profit = (number of tools sold)(revenue per tool) – [fixed cost + (number of tools made)(cost per tool)]

P = 20,000 x 8 – [10,000 + (3 x 20,000)]

P = 20,000 x 8 – [10,000 + (3 x 20,000)]

P = 160,000 – [10,000 + 60,000]

P = 160,000 – 70,000

P = 90,000

We have a profit of $90,000 for selling 20,000 tools, but remember that we need to determine the profit PER TOOL. To calculate this, we divide the total profit of $90,000 by the number of tools produced, which is 20,000. We have:

$90,000/20,000 = $9/2 = $4.50

Answer C.

Fixed cost = $10,000
Selling price is $8/tool and production cost is $3/tool.
$(8-3) = $5(Profit)

5*20,000 = $100,000
$100,000-$10,000(FC) = $90,000(Gross profit.)

Gross profit/tool = $90,000/20,000 = 4.5

C.

We are trying to find out the profit per tool. Lets do this withou having to do a lot of math. Here is a simple way, we only divide once and the rest is given on the statement.

The statement tells us the selling of each tool $8.00 now we need to get the cost. We already know that each tool has a fixed cost of $3.00 and each batch is $10,000.

The only thing we actually need to do here is take allocate the $10,000 to each tool and then add it to the $3.00 cost per tool stated.

Lets divided the cost of the batch per tool: 20,000/ $10,000 = $0.50 per tool.

Voila! We have $8.00 - ($3.00 + $0.50) = $4.50

Here's how this can be solved as well - If you prefer Algebra

Let n = Number of tools sold

Cost Price = 10,000 + 3n
Revenue = 8n
Gross profit = 8n - (10,000+3n) = 5n - 10,000

Gross Profit per tool = \(\frac{(5n-10,000)}{n}\) = \(5 - \frac{10,000}{n}\)

Plugging in given

Profit per tool = \(5 - \frac{10,000}{20,000} = 5 - \frac{1}{2} = 4.5\)

Answer Choice : C

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Answer: Option C

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