Question

Total Cost Analysis

The manager of a rival T-shirt stand found that her cost to produce 10 T-shirts is $107.09, while the cost to produce 40 T-shirts is $402.16..

Assume the cost​ C(x) is a linear function of​ x, the number of T-shirts produced.

Find the total cost of producing 100 T-shirts.(Round to 2 decimal places)

Answer 1

Here, since cost is a linear function of x, so we will will use the high low method to calculate the variable cost, fixed cost and then total cost.

In high low method, first we calculate the variable cost per unit by the following formula:

Variable cost per unit = Highest activity cost - Lowest activity cost / Highest number of shirts - Lowest number of shirts

We have,

Highest activity cost = $402.16

Highets number of shirts = 40

Lowest activity cost = $107.09

Lowest number of shirts = 10

Now, putting these values in the above formula, we get,

Variable cost per shirt = ($402.16 - $107.09) / 40 - 10

Variable cost per shirt = $295.07 / 30

Variable cost per shirt = $9.83567

Now, we will calculate fixed cost as per below:

Fixed cost = Highest activity cost - (Variable cost * Highest activity days)

Putting the values in the above formula, we get,

Fixed cost = $402.16 - ($9.83567 * 40)

Fixed cost = $402.16 - $3934267

Fixed cost = $8.733

Now, the cost function is:

C (x) = $8.733 + $9.83567x

where, x is the number of T shirts produced

Now,

Cost of producing 10 T shirts is:

Putting the values in the above cost function, we get,

C (10) = $8.733 + ($9.83567 * 10)

C (10) = $8.733 + $98.3567 = $107.09

So, cost of producing 10 T shirts is $107.09.