The Congress Company has identified two methods for producing playing cards. One method involves using a machine having a fixed cost of $10,000 and variable costs of $1.00 per deck of cards. The other method would use a less expensive machine (fixed cost = $5,000), but it would require greater variable costs
($1.50 per deck of cards). If the selling price per deck of cards will be the same under each method, at what level of output will the two methods produce the same net operating income?
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A. B. C. D. E.Explanation
Total cost(Method 1) = $1.00(Q) + $10,000.
Total cost(Method 2) = $1.50(Q) + $5,000.
Set equal and solve for Q: Q + $10,000 = $1.50(Q) + $5,000
$5,000 = $0.5(Q)
10,000 = Q.
To find the level of output at which the two methods produce the same net operating income, we need to compare the costs and revenues of each method.
Let's start by calculating the total cost for each method at different levels of output.
Method 1 (Machine with fixed cost of $10,000 and variable cost of $1.00 per deck): Total Cost = Fixed Cost + (Variable Cost per unit * Number of decks)
Method 2 (Machine with fixed cost of $5,000 and variable cost of $1.50 per deck): Total Cost = Fixed Cost + (Variable Cost per unit * Number of decks)
We know that the selling price per deck of cards will be the same under each method. Let's assume the selling price per deck is "P".
Now, let's calculate the net operating income for each method at different levels of output:
Method 1 Net Operating Income = (Selling Price per deck * Number of decks) - Total Cost for Method 1
Method 2 Net Operating Income = (Selling Price per deck * Number of decks) - Total Cost for Method 2
We want to find the level of output where the net operating incomes are equal:
Method 1 Net Operating Income = Method 2 Net Operating Income
Now, let's solve the problem by substituting the given values.
Method 1: Fixed Cost = $10,000 Variable Cost per deck = $1.00
Method 2: Fixed Cost = $5,000 Variable Cost per deck = $1.50
Selling Price per deck = P (unknown)
Method 1 Net Operating Income = (P * Number of decks) - (10,000 + (1.00 * Number of decks))
Method 2 Net Operating Income = (P * Number of decks) - (5,000 + (1.50 * Number of decks))
We want to find the level of output (Number of decks) where Method 1 Net Operating Income equals Method 2 Net Operating Income.
Set the equations equal to each other:
(P * Number of decks) - (10,000 + (1.00 * Number of decks)) = (P * Number of decks) - (5,000 + (1.50 * Number of decks))
Simplify the equation:
-10,000 - (1.00 * Number of decks) = -5,000 - (1.50 * Number of decks)
Combine like terms:
-10,000 + 5,000 = -1.50 * Number of decks + 1.00 * Number of decks
-5,000 = -0.50 * Number of decks
Divide both sides by -0.50:
Number of decks = 10,000
Therefore, the two methods will produce the same net operating income at a level of output of 10,000 decks.
The correct answer is D. 10,000 decks.