Question

A manufacturer sells a product for $10 per unit. The manufacturer's variable costs are $5 per unit and the fixed cost is $1000. How many units must the manufacturer produce each month to break even?

Max 2A + 3B s.t. 1A + 2B S 6 5A + 3B

Answer 1

To break even, the manufacturer must produce 200 units each month

Explanation:

To break even, the amount of total cost must be the same as the amount of revenues.

Total Cost is Fixed cost plus unitary variable cost multiplied by the produce quantity.

Total cost= FC + vc*Q

Where ,

FC=Fixed cost

vc=unitary variable cos

Q=produce quantity

Revenue= Price * Q

Break even FC + vc*Q=Price * Q

Isolating Q

FC=(Price * Q)-(vc*Q)

FC=(Price-vc) * Q

Q= FC/(Price-vc)

Q= $1000/($10-$5)

Q= $1000/$5

Q= 200 units

Answer 2

200 units

Explanation:

The total income must be at least equal to the costs, and that is:

10*U = 5*U + 1000 Solving for U, which is the amount of units sold per month:

U = 1000/5 = 200 units.