Question

Jose Foster, a manager of Prettiest Pooch, Inc., was reviewing the water bills of a dog daycare and spa. He determined that its highest and lowest bills of $3,800 and $2,000 were incurred in the months of May and November, respectively. If 600 dogs were washed in May and 200 dogs were washed in November, what was the fixed cost associated with the company's water bill? (Round any intermediate calculations to the nearest cent and your final answer to the nearest dollar.)

A) $2,000
B) $3,800
C) $1,100
D) $1,800

Answer 1

The fixed cost associated with Prettiest Pooch, Inc.'s water bill is $1,100, which is derived from comparing the water bill costs attributed to the number of dogs washed in May and November.

Step-by-step explanation:

José Foster, the manager of Prettiest Pooch, Inc., wants to figure out the fixed cost component of the company's water bills, given the highest bill of $3,800 for 600 dogs washed in May and the lowest bill of $2,000 for 200 dogs washed in November. To calculate the fixed cost, we first need to determine the variable cost per dog washed by using the given water bill amounts and the number of dogs washed each month.

To calculate the variable cost per dog, we'll use the water bill from May and November:

• Variable cost in May: ($3,800 - Fixed Cost) / 600 dogs
• Variable cost in November: ($2,000 - Fixed Cost) / 200 dogs

Since the variable cost per dog wash must be the same each month, we can set the two expressions equal to each other and solve for the Fixed Cost. If ($3,800 - Fixed Cost) / 600 = ($2,000 - Fixed Cost) / 200, We can multiply both sides by 600 * 200 to eliminate the denominators:

200 * ($3,800 - Fixed Cost) = 600 * ($2,000 - Fixed Cost)

760,000 - 200 * Fixed Cost = 1,200,000 - 600 * Fixed Cost

Combining like terms gives us:

760,000 - 1,200,000 = 600 * Fixed Cost - 200 * Fixed Cost

-440,000 = 400 * Fixed Cost

Dividing both sides by 400 we get:

Fixed Cost = - $1,100

So the fixed cost associated with the company's water bill is $1,100, which matches option C. Fixed costs are the costs that do not change with an increase or decrease in the amount of goods or services produced. In this scenario, Fixed Cost is the cost Prettiest Pooch, Inc. would incur no matter how many dogs they wash.