terp26 wrote:
The total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X’s gross profit per tool is
(A) $3.00
(B) $3.75
(C) $4.50
(D) $5.00
(E) $5.50
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.
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