If a firm has the following cost and revenue functions, find the break-even points.
A) Break-even values are at and units.
B) Break-even values are at and units.
C) Break-even values are at and units.
D) Break-even values are at and units.
E) Break-even values are at and units.

Question

If a firm has the following cost and revenue functions, find the break-even points. ​  ​
A) Break-even values are at and units. 
B) Break-even values are at and units. 
C) Break-even values are at and units. 
D) Break-even values are at and units. 
E) Break-even values are at and units.

Quizplus · Accepted Answer

The break-even point is where the total cost equals total revenue.

Total cost = Fixed cost + Variable cost
Total revenue = Price x Quantity

From the given cost and revenue functions, we have:

Fixed cost = 5000
Variable cost = 200q
Price = 12 - 0.01q

Setting total cost equal to total revenue, we get:

5000 + 200q = (12 - 0.01q)q
5000 + 200q = 12q - 0.01q^2
0.01q^2 - 188q + 5000 = 0

Solving for q using the quadratic formula:

q = (188 ± sqrt(188^2 - 4(0.01)(5000))) / (2(0.01)) 
q ≈ 630.10 or q ≈ 7874.90

Therefore, the break-even values are at approximately 630.10 and 7874.90 units.

Option E is the closest to the exact values, and therefore the best choice.

If a Firm Has the Following Cost and Revenue Functions