Questions: A manufacturer of 24-hr variable timers, has a monthly fixed cost of 35000 and a production cost of 6 for each timer manufactured. The units sell for 11 each. Find the break-even point algebraically. a. none of these b. break-even production 7000 units; break-even revenue 77,000 c. break-even production 70000 units; break-even revenue 77,000 d. break-even production 70000 units; break-even revenue 770,000 e. break-even production 7000 units; break-even revenue 770,000

Solution Steps

To find the break-even point, we need to determine the number of units where total cost equals total revenue. The total cost is the sum of the fixed cost and the variable cost per unit times the number of units. The total revenue is the selling price per unit times the number of units. Set these two expressions equal and solve for the number of units.

The total cost \( C(x) \) for producing \( x \) units is given by the sum of the fixed cost and the variable cost per unit: \[ C(x) = 35000 + 6x \]

The total revenue \( R(x) \) from selling \( x \) units is given by the selling price per unit times the number of units: \[ R(x) = 11x \]

To find the break-even point, set the total cost equal to the total revenue: \[ 35000 + 6x = 11x \]

Rearrange the equation to solve for \( x \): \[ 35000 = 11x - 6x \] \[ 35000 = 5x \] \[ x = \frac{35000}{5} \] \[ x = 7000 \]

Substitute \( x = 7000 \) into the revenue function to find the break-even revenue: \[ R(7000) = 11 \times 7000 = 77000 \]

Final Answer