Find the break-even point for the firm whose cost function C and revenue function R are given.
C(x) = 16x + 10,000; R(x) = 21x
To find the break-even point for the firm, we need to equate the cost function (C) and the revenue function (R) since at the break-even point, the firm's revenue is exactly equal to its cost.
Given:
Cost function, C(x) = 16x + 10,000
Revenue function, R(x) = 21x
To find the break-even point, we can set C(x) equal to R(x):
16x + 10,000 = 21x
Now, let's solve for x:
16x - 21x = -10,000 (subtract 21x from both sides)
-5x = -10,000 (combine like terms)
x = -10,000 / -5 (divide both sides by -5)
x = 2,000
The break-even point for the firm is when x is equal to 2,000 units. This means that the firm needs to sell 2,000 units to cover its costs and reach the break-even point.