Question

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. lf a batch of \[20,000\]tools is produced and sold, then Company X's gross profit per tool is:
\[\begin{array}{*{20}{l}}
  {A.{\text{ }}\$ 3.00} \\
  {B.{\text{ }}\$ 3.75} \\
  {C.{\text{ }}\$ 4.50} \\
  {D.{\text{ }}\$ 5.00} \\
  {E.{\text{ }}\$ 5.50}
\end{array}\]

Answer 1

Hint: Here, we will use the formulas for the total fixed cost, the total variable cost, the total cost, the total revenue and the gross profit to find the company’s gross profit per tool. The gross profit of a firm or company is equal to the total revenue minus the total cost.

Complete step-by-step answer:
According to the given question, we get to know that fixed cost per tool \[ = \$ 10,000\]
The variable cost per tool is \[\$ 3\].
The selling price per tool is \[\$ 8\].
The total number of tools in the batch is \[20,000\].
Now, the total fixed cost of \[20,000\] tools\[ = \$ 10,000\] (It does not vary because it is the fixed cost which is incurred even if there is no production.)
The total variable cost of \[20,000\] tools\[ = \$ (3 \times 20,000) = \$ 60,000\]
Therefore, the total cost of production
= Total Fixed cost + Total Variable cost
\[
   = \$ (10000 + 60000) \\
   = \$ 70,000 \\
\]
Total Revenue from \[20,000\] tools\[ = \$ (8 \times 20,000) = \$ 1,60,000\]
Total Gross Profit from \[20,000\] tools
=Total Revenue-Total cost
\[
   = \$ (160000 - 70000) \\
   = \$ 90,000 \\
\]
Now, gross profit per tool
\[
   = \dfrac{{Total{\text{ }}Gross{\text{ }}Profit}}{{No.{\text{ }}of{\text{ }}tools}} \\
   = \dfrac{{90000}}{{20000}} \\
   = \$ 4.50 \\
\]
Thus, the answer is option D.

Note: We notice that the fixed cost and the total fixed cost remains the same but the total variable cost is the product of the variable cost per tool and the total number of tools. This is because the fixed cost is not dependent on the production quantity. It is incurred even when there is no production, whereas, the variable cost is dependent on the quantity of production and varies accordingly. We need to remember that the gross profit per item is always the total gross profit divided by the total number of items.