The selling price for a felt-tip pen is $2 per pen. Fixed cost of the operation is $41,000 per month and variable cost is 60 cents per pen.a. Find the break-even quantity. (Do not round intermediate calculations. Round the final answer to the nearest whole number.)Break-even quantity units per monthb. How many pens must be sold to obtain a monthly profit of $24,000? (Do not round intermediate calculations. Round the final answer to the nearest whole number.)Quantity units per monthc. What is the break-even point in sales dollars? (Do not round intermediate calculations. Round the final answer to the nearest whole number.)BEP$ per monthd. Another type of marker with the following characteristics can also be produced by the machine: Selling price = $3 each, Variable cost = $0.90 each, and Proportion of revenue = 28%. Calculate the break-even point in sales dollars. (Do not round intermediate calculations. Round the final answer to 2 decimal places.)BEP$ per month
Question
The selling price for a felt-tip pen is 41,000 per month and variable cost is 60 cents per pen.a. Find the break-even quantity. (Do not round intermediate calculations. Round the final answer to the nearest whole number.)Break-even quantity units per monthb. How many pens must be sold to obtain a monthly profit of per monthd. Another type of marker with the following characteristics can also be produced by the machine: Selling price = 0.90 each, and Proportion of revenue = 28%. Calculate the break-even point in sales dollars. (Do not round intermediate calculations. Round the final answer to 2 decimal places.)BEP$ per month
Solution
a. To find the break-even quantity, we need to set total revenue equal to total cost and solve for the quantity. The total revenue is the selling price times the quantity (2Q), and the total cost is the fixed cost plus the variable cost times the quantity (41000 + 0.6Q). Setting these equal gives:
2Q = 41000 + 0.6Q 1.4Q = 41000 Q = 41000 / 1.4 Q = 29286 units per month (rounded to the nearest whole number)
b. To find the quantity needed for a monthly profit of $24,000, we need to set total revenue equal to total cost plus profit and solve for the quantity. This gives:
2Q = 41000 + 0.6Q + 24000 1.4Q = 65000 Q = 65000 / 1.4 Q = 46429 units per month (rounded to the nearest whole number)
c. The break-even point in sales dollars is the selling price times the break-even quantity. This gives:
BEP = $58572 per month
d. For the other type of marker, the break-even point in sales dollars is found by setting total revenue equal to total cost and solving for the revenue. The total revenue is the selling price times the quantity (3Q), and the total cost is the fixed cost plus the variable cost times the quantity (41000 + 0.9Q). Setting these equal gives:
3Q = 41000 + 0.9Q 2.1Q = 41000 Q = 41000 / 2.1 Q = 19524 units per month
The break-even point in sales dollars is then the selling price times the break-even quantity. This gives:
BEP = $58572 per month
The proportion of revenue is not needed to calculate the break-even point in sales dollars.
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