Question

Sawtimber is a term for trees that are suitable for sawing into lumber, plywood and other products. For the years 1983 - 1995, the unit value y (in dollars per million board feet)of one type of sawtimber harvested in California can be modeled by y = 0.125x? - 569x + 848000 where 400 5 x ≤ 2200 where x is the volume of timber harvested (in millions of board feet)

for what harvested timber volumes is the value of the timber less than $400,000 per million board feet?

Answer 1

Explanation:

We are given the equation:

y = 0.125x² - 569x + 848000

And we are asked to find the range of values of x for which y is less than $400,000 per million board feet.

Substituting $400,000 for y, we get:

$400,000 = 0.125x² - 569x + 848000

Simplifying this equation, we get:

0.125x² - 569x + 448000 = 0

Now, we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b² - 4ac))/(2a)

where a = 0.125, b = -569, and c = 448000.

Plugging in these values, we get:

x = (-(-569) ± sqrt((-569)² - 4(0.125)(448000)))/(2(0.125))

x = (569 ± sqrt(322961))/0.25

x = (569 ± 569.39)/0.25

x ≈ 1163.57 or x ≈ 68.43

However, we need to check if these values satisfy the given condition of 400 5 x ≤ 2200.

Only x ≈ 68.43 satisfies this condition. Therefore, the harvested timber volume for which the value of the timber is less than $400,000 per million board feet is approximately 68.43 million board feet.