Question

10. What are the break-even points of the profit function (the values of x where profit equals 0)? Use the quadratic formula. (4 points: 2 points for each x-value)

Answer 1

r = 50000

P (r) = 0.7r - 35000

Explanation:

Given cost function is

C (r) = 0.85r + 35000

and revenue function is

R (r) = 1.55r

At break even point, revenue is equal to cost

R(x)= C(x)

1.55r = 0.85r+35000

Subtract 0.85 from both sides

0.7r = 35000

divide by 0.7 on both sides

r = 50000

Profit function

P(x)= R(x)- C(x)

P(r) = 1.55r - (0.85r+35000)

P(r) = 1.55r - 0.85r - 35000

P(r) = 0.7r - 35000

Answer 2

The break-even points for the profit function are approximately x = 2.75 and x = -0.25.

The quadratic formula is a general formula for solving quadratic equations, which are equations of the form a
`x^2`+ bx + c = 0. The formula is:

x = (-b ± √(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

If the profit function is given by the equation 2
`x^2` - 5x - 3 = 0, you can plug the values of a, b, and c into the quadratic formula to get:

x = (5 ± √((-5)^2 - 4 * 2 * -3)) / (2 * 2)

x = (5 ± √(49 + 24)) / 4

x = (5 ± √73) / 4

Therefore, the break-even points for this profit function are approximately x = 2.75 and x = -0.25.