Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.)
A)254 units
B)254 units or 281 units
C)272 units
D)281 units
E)no real solution

Question

Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.) 
A)254 units 
B)254 units or 281 units 
C)272 units 
D)281 units 
E)no real solution

Quizplus · Accepted Answer

The formula for break-even sales is R = C, or revenue equals cost. Since we are given a cost function C and a revenue function R, we can set them equal to each other in order to find the break-even point.

Here are the steps:

1. Start with the cost function:

C(x) = 520x + 2,880

2. Set up the revenue function, which is the price per unit times the number of units sold:

R(x) = 5x

3. Set R(x) equal to C(x):

5x = 520x + 2,880

4. Solve for x:

515x = 2,880

x = 5.6

5. Round x up to the nearest whole unit, since we can't sell a fraction of a unit:

x = 6

Therefore, we need to sell 6 units in order to break even. The correct answer choice is D, since 281 is the closest whole number to 5.6 when rounded up.

Find the Sales Necessary to Break Even (R - C