A manager must decide between two location alternatives, Boston and Chicago. Boston would have annual fixed costs of $70,000, transportation costs of $60 per unit, and labor and material costs of $200 per unit. Chicago would have annual fixed costs of $90,000, transportation costs of $40 per unit, and labor and material costs of $170 per unit. Revenue will be $300 per unit. (You need to show your work, rather than just a final answer.)
(A) Which alternative would yield the higher profit for an annual demand of 3,000 units?
(B) Would the two locations yield the same profit at a certain volume? If so, at what volume would that be?

Solution and Explanation:

(a) profit at 3,000 units at Boston: Revenues = 3,000 multiply 300 = $900,000

annual fixed costs = 70,000 transport = 60 multiply 3,000 = 180,000 labour/material = 600,000. Total costs = 850,000

Profit = 900,000 - 850,000 = $50,000

profit at Chicago: Revenues = 3,000 multiply 300 = $900,000

annual fixed costs = 90,000 transport = 40 multiply 3,000 = 120,000 labour and material = 170 multiply 3,000 = 510,000. Total costs = 720,000

Profit = 900,000 minus 720,000 = $180,000

(b) as the revenue per unit is same, profits will be equal when costs are equal. Assuming the volume to be x units.

Costing at boston = 70,000 plus 60x plus200x = 70,000 plus 260x

Costing at chicago = 90,000 plus 40x plus 170x = 90,000 plus 210x

Now 70,000 plus 260x = 90,000 plus 210x

20,000 = 50x or x = 400 units

where is the graph?