Question

Candy bars are sold in a local store for 60 cents each. The factory has $1000 in fixed costs plus 10 cents of additional expense for each candy bar made. Assuming all candy bars manufactured can be sold, find the break-even point?

Answer 1

Produce of `2000` Candy bars is the break even point.

Explanation:

Break-even point is the number of units `N` produced and sold

which make zero profit.

Revenue earned , `R=P*N; P=$0.6` is unit price.

`P*N – (V * N + F) = 0 ; V=$0.1,F=$1000 ; V and F` are

additional cost per unit and fixed cost respectively.

`P*N – (V * N + F) = 0 or N(P-V)=F:. N= F/(P-V)`

So, break-even point is

`N = F/(P- V)= 1000/(0.6-0.1)=2000` Candy bars. [Ans]

Answer 2

2000 bars at $1200

Explanation:

Total selling income = manufacturing cost

Before we begin; notice we have a mixture of units. Cents and dollars. Consequently we need to express these using just one unit of measurement. I choose dollars.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let the count of bars be `n`

Total selling income `=nxx$0.60 -> $(0.60n)`

Production cost `=$1000+(nxx$0.10) -> $(0.1n+1000)`

Setting one against the other for break even point.

Dropping the dollar sign as we will just end up with a count (n)

`0.1n+1000=0.6n`

`0.6n-0.1n=1000`

`0.5n=1000`

`n=1000/0.5 = 2000`

`color(blue)("Check")`

`$0.6xx2000 = $1200`
`($0.1xx2000)+$1000 = $1200`