Question

Where - R - U produces global positioning systems (GPS) that can be used in a car. The expense equation is E=-5,000p+$8,300,000, and the revenue equation is R = -100p^2 + 55,500p. Determine the prices at the breakeven points. Round to the nearest cent.

Option 1: $3,300
Option 2: $7,000
Option 3: $10,000
Option 4: $11,100

Answer 1

The prices at the breakeven points for Where - R - U's GPS systems are approximately $3,300 and $10,000 after setting the expense equation equal to the revenue equation and solving for p.

Step-by-step explanation:

To determine the prices at the breakeven points for Where - R - U's GPS systems, we set the expense equation equal to the revenue equation and solve for p. The expense equation is E = -5,000p + $8,300,000, and the revenue equation is R = -100p2 + 55,500p.

At breakeven, E = R, so we have:

-5,000p + $8,300,000 = -100p2 + 55,500p

Adding 100p2 to both sides and subtracting 55,500p from both sides, we get:

100p2 - 60,500p + $8,300,000 = 0

Using the quadratic formula, we solve for p to find the two prices that will give us the breakeven points:

p = [-(-60,500) ± √ ((-60,500)2 - 4(100) ($8,300,000))]/ (2(100))

After calculations and rounding to the nearest cent, the two prices are approximately $3,300 and $10,000. Therefore, Options 1 and 3 are the correct prices at the breakeven points.