Applied problems

pullagurla 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 pro� t 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 proï¬� t per
tool is
(A) $3.00
(B) $3.75
(C) $4.50
(D) $5.00
(E) $5.50

We can use the following formula:

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

Since the total profit is $90,000 and 20,000 tools are produced and sold, the profit per tool is 90,000/20,000 = 9/2 = $4.50

Alternate Solution:

If there were no fixed costs, the profit per tool would be the selling price minus the cost to make each tool, or $8 - $3 = $5. However, the total fixed cost of $10,000 must be “absorbed” by the tools that are sold. Since 20,000 tools were sold, the fixed cost that each tool must “absorb” is $10,000/20,000, or $0.50 per tool. Thus, the profit per tool is $8 - $3 - $0.50 = $4.50.

Answer: C