Julius builds dining chairs that he sells for $200 a chair. His fixed costs are $1,000 (for workshop equipment). Each chair costs him $50 in materials to produce plus an extra $25 for each previous chair made that day which reflects Julius' increasing exhaustion. (Thus, the first chair cost $50, the second costs $75, the third cost $100, etc.) Assume time requirements in producing a chair are not a factor. How many chairs should Julius produce each day?

Question

Quizplus · Accepted Answer

Let's first calculate Julius' costs per chair:

Variable costs: $50 + $25(previous chair cost) = $75
Total cost: $75 + $1,000 (fixed cost) = $1,075

Now let's calculate his revenue per chair:

Revenue: $200

Profit per chair: Revenue - Total cost = $200 - $1,075 = -$875

As we can see, Julius is currently making a loss on each chair he produces. To break even (i.e. make $0 profit but also not lose any money), Julius needs:

Revenue = Total cost
$200Q = $75Q + $1,000
$125Q = $1,000
Q = 8

Julius needs to produce 8 chairs per day to break even. However, to make a profit, he needs to produce even more chairs. Therefore, the closest option to 8 is 7 and since it is the only option listed, the answer is C.

Julius Builds Dining Chairs That He Sells for $200 a Chair