Question

Use the equations for the total cost c and total revenue r to find the number x of units a company must sell to break even. (round to the nearest whole unit.) c = 7.9 x 7,000, r = 5.26x

Answer 1

The company must sell approximately 3,348 units to break even.

Step-by-step explanation:

To find the break-even point, we set the total cost (c) equal to the total revenue (r) and solve for the number of units (x). The equation is
`\(7.9x = 5.26x * 7,000\). Simplifying, we get \(7.9x = 36,820\).` Dividing both sides by 7.9, we find
`\(x \approx 4,657.97\)`. Since the number of units must be a whole number, rounding to the nearest whole unit gives us approximately 3,348 units.

In this context, the break-even point is the number of units the company needs to sell to cover its total costs with total revenue. The equation
`\(7.9x\)` represents the total cost, which includes both fixed and variable costs per unit. The equation
`\(5.26x\)` represents the total revenue, where
`\(5.26\)` is the revenue generated per unit.

By setting these two equations equal to each other, we find the quantity of units that will make total revenue equal to total cost. In practical terms, the company needs to sell around 3,348 units to neither profit nor incur a loss. This analysis helps businesses understand the sales volume required to cover all expenses and reach the break-even point.