Cost Accounting Break Even Question Need Help

Question

Trenton and Company makes a single product requiring $50 of direct materials. Manufacturing overhead is applied using a predetermined overhead of 150% of direct labor cost. One third of manufacturing overhead is fixed. There is no under or over applied overhead and the company has no beginning or ending inventory. The company reports the following results for August :
Number of Units Sold : 8,000
Selling Price Per Unit : $300
Manufacturing Cost Per Unit : $200
Variable Selling and Admin. Expenses per unit : $45
Total Fixed Selling and Admin Expenses : $290,000
Question : How many units can sales go down before company incurs a loss?
A) 1765 B) 5,100 C) 2,700 D) 6,235 E ) None
HELP I RECEIVED : You have mixed the concepts of breakeven analysis and absorption costing. Breakeven analysis relies on direct costing
Contribution margin is an important concept so is fixed cost

manufacturing cost is $50 fixed and $100 variable
contribution margin is 300-(200-50+45) = 105

290,000/105 = 2762 * 300 = 828,571 this is the breakeven point, the breakeven point is the $sales or number of units that must be sold to cover expenses.

MY FOLLOW UP THINKING : I tried dividing 828,571 by 300 and got 2761 but this was not the right answer of 1765 please help with steps on how to get this

Answer 1

something is amiss here.

1. either the "direct materials" are included in the "manufacturing cost per unit", or that number is irrelevant

2. the "overhead" number of 150% of "direct labor cost" is meaningless because no labor cost is shown

3. the comments about inventory are unrelated to the problem

 

We know that Break even in units = Fixed costs / (unit selling price - variable costs)

 

if the given answer is correct, we can use that number to solve for variable costs, and the equation would be

1765u = $290,000 / ($300/u - VC/u); solving that equation will give us a Variable Cost of $253.49/unit.

 

BUT, the given information leads us to a Variable Cost of $245/u, which leads us to BE of 5,272 units, which, when subtracted from 8,000 units leaves 2,727, which is close to option C