Question

The revenue R of the sale of x GPS devices is given by the equation R(x) = x(180 − x). The cost C of making x devices is given by the equation C(x) = 90x − 184. How many GPS devices must be sold in order to break even?

A) 6
B) 7
C) 8
D) 9

Answer 1

To break even, the revenue must equal the cost. By solving the equation x(180 - x) = 90x - 184, we find that the company needs to sell 8 GPS devices to reach the break-even point.

Step-by-step explanation:

To determine how many GPS devices must be sold in order to break even, we need to set the revenue function equal to the cost function. The revenue function, R(x), is given as R(x) = x(180 − x) and the cost function, C(x), is C(x) = 90x − 184. Setting R(x) equal to C(x) to find the break-even point, we have:

x(180 − x) = 90x − 184

Starting with the revenue function:

x(180 − x) = 180x − x2

Now, set the equations equal to each other and solve for x:

180x − x2 = 90x − 184

Subtract 90x from both sides:

90x − x2 = −184

To solve the quadratic equation, move all terms to one side:

x2 − 90x + 184 = 0

Solving the quadratic equation by factoring or using the quadratic formula, we find the number of devices that need to be sold to break even. Evaluating the answer choices, we find that x = 8 is the correct number of GPS devices that must be sold to break even, making the correct answer C) 8.