Question

Shipping expense is $9,000 for 8,000 kilograms shipped and $11,250 for 11,000 kilograms shipped. Assuming that this activity is within the relevant range, if the company ships 9,000 kilograms, its expected shipping expense would be closest to which of the following?

a. $9,972
b. $10,125
c. $9,750
d. $8,583

Answer 1

To find the expected shipping expense for 9,000 kilograms, a linear equation based on the cost per kilogram is used. The slope is calculated to be $0.75/kg, and using the first provided data point, the expense for 9,000 kilograms is estimated to be closest to $9,750.

Step-by-step explanation:

To estimate the expected shipping expense for 9,000 kilograms, we can use a linear equation based on the two given points: (8,000 kg, $9,000) and (11,000 kg, $11,250). First, let's find the variable cost per kilogram.

1. Calculate the slope (cost per kilogram), which is the change in cost divided by the change in kilograms.
2. Subtract the cost at the lower amount of kilograms from the cost at the higher amount, and divide by the difference in kilograms.
   Slope = ($11,250 - $9,000) / (11,000 kg - 8,000 kg) = $2,250 / 3,000 kg = $0.75/kg
3. Now that we have the variable cost per kilogram, we can use the point-slope form to create an equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points.
4. Using the first point (8,000 kg, $9,000), the equation becomes: y - $9,000 = $0.75/kg (x - 8,000 kg).
5. Substitute x with 9,000 kg to find the expected shipping expense for 9,000 kilograms:
   Expected Shipping Expense = $9,000 + ($0.75/kg × (9,000 kg - 8,000 kg))
6. Calculate the result: Expected Shipping Expense = $9,000 + ($0.75/kg × 1,000 kg) = $9,750.

The expected shipping expense for shipping 9,000 kilograms is closest to $9,750, which makes option c the correct answer.