Question

The cost to produce x units of wire is C = 35x + 500, while the revenue is R = 60x.

Find all intervals where the product will at least break even.


Select the correct choice below and, if necessary, fill in the answer box to complete your choice.


A. The inequality in interval notation is


B. The product will never break even.

Answer 1

The product will at least break even when 20 or more units are produced. The inequality in interval notation expressing this condition is [20, ∞).

Step-by-step explanation:

To determine when the product will at least break even based on the production cost function C = 35x + 500 and the revenue function R = 60x, we need to find the values of x (units of wire) for which total revenue equals or exceeds total cost, that is, R ≥ C. We can set up the inequality:

60x ≥ 35x + 500

Subtract 35x from both sides of the inequality to isolate the variable on one side:

25x ≥ 500

Divide both sides by 25 to solve for x:

x ≥ 20

The inequality in interval notation is [20, ∞), indicating that the product will break even when 20 or more units are produced. Therefore, the correct choice is:

A. The inequality in interval notation is [20, ∞).

Answer 2

n order for the product to at least break even, the revenue must be equal to or exceed the cost. To solve for this interval we set R>=C. So,

45x>=20x+550. Once we solve this equation we get x>=22 so the interval where the product will at least break even

so the answer is B.