A firm has two plantsX and Y producing the same product whic

A firm has two plants(X and Y) producing the same product which sells for $12 each. Fixed costs are $5,000/year at plant X and $7,000/year at plant Y and variable costs are $3.00/unit and $2.00/unit for X and Y, respectively. The total profit at X and Y are equal when the volume of each plant(units) is:

Solution

let the volume at plant X is x and at plant Y be y

then the profit for plant X is 12x-5000-3x

and at plant Y 12y - 7000-2y

since profits are equal, we have 12x-5000-3x = 12y - 7000-2y

i.e., 10y - 9x = 2000 (on simplifing)

hence the volume at each plant must be 2000 units