At a selling price of $ 54 , a lamp company breaks even on total sales of $ 3564 . If the company's overhead is $ 396 , find the marginal production cost per lamp and find the profit on sales of 145 lamps.
To find the marginal production cost per lamp, we need to consider the break-even point and the overhead cost.
The break-even point is the point at which the company neither makes a profit nor incurs a loss. In this case, the break-even point is given as $3564 in total sales.
Let's assume the production cost per lamp is C and the number of lamps sold is L.
The total sales can be calculated by multiplying the selling price per lamp (given as $54) by the number of lamps sold:
Total sales = Selling price per lamp × Number of lamps sold
= $54 × L
Since the break-even point occurs when the company neither makes a profit nor incurs a loss, the total sales should be equal to the total costs.
Total costs = Total fixed costs + Total variable costs
= Overhead costs + (Marginal production cost per lamp × Number of lamps sold)
= $396 + (C × L)
Since the total sales and the total costs at the break-even point are equal, we can set up the equation as follows:
$54 × L = $396 + (C × L)
Now, we can solve for the marginal production cost per lamp (C):
$54 × L - C × L = $396
L × ($54 - C) = $396
C = $54 - $396/L
To find the profit on the sales of 145 lamps, we need to consider the selling price, the production cost, and the overhead cost.
Let's substitute the given values into the equation we obtained earlier:
C = $54 - $396/145
Now we can calculate the marginal production cost per lamp:
C = $54 - $2.73
C ≈ $51.27
To find the profit on the sales of 145 lamps, we need to subtract the total cost (including the overhead cost) from the total sales.
Total cost = Overhead cost + (Marginal production cost per lamp × Number of lamps sold)
= $396 + ($51.27 × 145)
= $396 + $7446.15
≈ $7842.15
Profit = Total sales - Total cost
= (Selling price per lamp × Number of lamps sold) - Total cost
= ($54 × 145) - $7842.15
≈ $7830 - $7842.15
≈ -$12.15
The profit on sales of 145 lamps is approximately -$12.15. This negative value indicates a loss rather than a profit.