Question

To break even in a manufacturing​ business, income or revenue R must equal the cost of production C. The revenue R from selling x number of computer boards is given by R=40x​, and the cost C of producing them is given by C=30x+1000. Find how many boards must be sold to break even. Find how much money is needed to produce the​ break-even number of boards.

Answer 1

To find the number of boards that must be sold to break even, we need to set the revenue equal to the cost and solve for x.

Given:

Revenue R = 40x

Cost C = 30x + 1000

Since the break-even point is when revenue equals cost, we have the equation:

40x = 30x + 1000

To solve for x, we subtract 30x from both sides of the equation:

40x - 30x = 30x + 1000 - 30x

Simplifying:

10x = 1000

Dividing both sides by 10:

x = 100

Therefore, to break even, 100 computer boards must be sold.

To find the amount of money needed to produce the break-even number of boards, we substitute the value of x into the cost equation:

C = 30x + 1000

C = 30 * 100 + 1000

C = 3000 + 1000

C = 4000

Therefore, $4000 is needed to produce the break-even number of boards.

Explanation: