**Answer:**

$188,000

**Explanation:**

To solve this exercise we will use the "High Low Method" which is a technique that allows to determine the costs associated with a certain level of activity, identifying its fixed and variable elements. This is done by taking the two most "extreme" data (the highest and the lowest) from a data set.

We will follow these steps:

** 1. Identify the data set:
**

** Cost Units
**

**90% occupancy ** $ 200,000 450

**80% occupancy** $ 197,000 400

Because it is a 500-unit apartament complex, with an occupancy level of 90%, it means that there are 450 units in operation, and with an occupancy level of 80%, 400.

A 50% occupancy level implies that there are 250 units in operation. Therefore, we want to find the total cost associated with the maintenance of these units.

**2. Identify the extreme data.
**

According to the data set, the most extreme are:

The highest cost is $ 200,000 and the highest number of units is 450.

The lowest cost is $ 197,000 and the lowest number of units is 400.

**3. Calculate the variable cost per unit.
**

For this we follow the following formula
:

Where HC = Highest Cost, LU= Lowest Cost, HU = Highest number of Units, LU = Lowest number of Units.

We replace
:

**VCU **= **$ 60** per unit.

**4. Calculate the fixed cost
**

Any level of activity is chosen. Here we will choose the highest: 450 units that operate at a cost of $ 200,000. Although we could choose the 400 units that operate at $ 197,000. It does not matter which one.

Now what we do is apply the following formula:

Where HC = Highest Cost, VCU = Variable Cost per Unit, HU = Highest number of Units.

We replace:

FC = 200,000 - ($ 60 * 450)

FC= 200,000 - (27,000)

**FC = 173,000
**

**5. Calculate the total variable cost of the new activity
**

We multiply the Variable Cost per Unit ($ 60) by the number of units that will operate at a 50% occupancy level (250)

**Variable cost of the new activity** = $ 60 * 250

**Variable cost of the new activity = $ 15,000
**

**6. Calculate the total cost
**

The fixed cost ($ 173,000) and the total variable cost of the new activity ($ 15,000) are added

**Total cost = **$ 173,000 + $ 15,000 = **$ 188,000**

This is the final answer.