Question

Given the cost function Upper C (x )and the revenue function Upper R (x )​, find the number of units x that must be sold to break even. Upper C (x )equals12xplus56 comma 000 and Upper R (x )equals16x.

Answer 1

The correct answer is 14000 units.

Explanation:

Cost function of x number of units sold is given by C(x) = 12x + 56000

Revenue function is given by R(x) = 16x

We need to find the number of units sold in order to break even. That invariably means we need to find the number of units at which the cost is equal to revenue or the profit is zero.

Thus profit π = R(x) - C(x) = 16x - 12x - 56000 and this is supposed to be equal to zero.

∴ 4x - 56000 = 0

⇒ 4x = 56000

⇒ x = 14000

Thus 14000 units of the goods needs to be sold to break even.