Callie's Gym is a complete fitness center. Owner Callie Ducain employs various fitness trainers who are expected to staff the front desk and to teach fitness classes. While on the front desk, trainers answer the phone, handle walk-ins and show them around the gym, answer member questions about the weight machines, and do light cleaning (wiping down the equipment, vacuuming the floor). The trainers also teach fitness classes (e. g., pilates, spinning, body pump) according to their own interest and training level. The cost of the fitness trainers is $600 per month and $30 per class taught. Last month, 100 classes were taught and five trainers were employed.

Required:

(1) Develop a cost equation for total cost of labor.

(2) What was total variable labor cost last month?

(3) What was total labor cost last month?

(4) What was the unit cost of labor (per class) for last month?

(5) What if Callie increased the number of classes offered by 50 percent?

a) Total Labor Cost = $600x + $30y.

b) Total variable cost = $3000.

c) Total labor cost last month = $6000.

d) Unit cost of labor per class = $60.

e) Total variable labor cost = $30 * 150 = $4500, Total Labor Cost = $3000 + $4500 = $7500, and Unit cost of labor per class = $7500/150 = $50.

Step-by-step explanation:

a) It is given that the labor cost includes two components: cost of trainers, which is actually their salaries, and cost of a fitness class taught. Fitness trainer costs $600 and one fitness class costs $30. Assuming there are x number of trainers and y number of classes, therefore the model can be expressed as:

Total Labor Cost = Fitness Trainer Cost * number of trainers + Fitness Class Cost * number of classes.

Total Labor Cost = $600x + $30y.

b) The total variable labor cost will be the cost spent on the number of classes. Since number of classes are 100 and the cost of one class is $30, therefore:

Total variable cost = cost of one class * number of classes.

Total variable cost = $30 * 100.

Total variable cost = $3000.

c) Furthermore, last month, x = 5 and y = 100. Plug these values in the total labor cost equation:

Total labor cost last month = $600 (5) + $30 (100).

Total labor cost last month = $3000 + $3000.

Total labor cost last month = $6000.

d) The total labor cost is $600. Number of classes are 100. Therefore:

Unit cost of labor per class = Total Labor Cost/Number of classes.

Unit cost of labor per class = $6000/100.

Unit cost of labor per class = $60.

e) If the number of classes are increases by 50%, this means that the number of classes will be 150 instead of 100. Therefore:

Total variable labor cost = $30 * 150 = $4500.

Total Labor Cost = $3000 + $4500 = $7500.

Unit cost of labor per class = $7500/150 = $50!