Food and Fitness (F&F) offers three different personal training packages to its customers.The packages provide for weekly sessions with specialists who provide nutrition supplies and personal training, where the supplies and training are both customized to meet the needs of each customer.The three packages include various combinations of these services.Package A includes the most time with specialists and an extensive package of nutrition supplies, Package B includes almost as much time with specialists but a very limited supply of nutrition supplies, and Package C includes only a limited time with specialists but a larger package of nutrition supplies.

F&F carefully tracks the average cost of nutrition supplies and the average amount of specialist time for each package, as shown in the table below.The total employment cost, including benefits, for the specialists is $40 per hour and the costs in the table reflect the number of 15 minute blocks of consultant time required for each package, namely 4 blocks for package A, 3 blocks for package B, and 1 block for package C.

F&F also spends a total of $2,400 per week to rent, heat, light, insure, and staff the building where the consultations and personal training take place.F&F expects to grow substantially over the coming years, so the current facilities are much larger than is required for the current level of activity.F&F believes that each customer places approximately the same load on the facilities, regardless of which package has been purchased, so facilities costs are allocated based on the number of customers.The current number of customers is 120, so the facilities cost per customer is $2,400 / 120 = $20/customer, as shown in the table below.

The F&F accounting system shows the following revenue, costs, and profit for each the three personal training packages:

Table 1

ABC

Package selling price$100$80$50

Package costs

Specialist time$40$30$10

Nutrition supplies$20$ 5$15

Facilities cost202020

Profit20255

The specialists are key to this business model as they have the technical training on the interaction between nutrition and exercise to effectively serve customers.Demand for the F&F packages is strong.F&F is currently turning away potential customers because their two specialists, each with available time for consultations of 40 hours per week, for a total available time for the two specialists of 80 hours per week, are completely booked.

Table 2

ABCTotals

# of customers purchasing package404040120

x Specialist hours per package1.0.75.25

Hours required40301080

Required:

1. (5 points) Calculate weekly profit based on the current mix of packages sold, as shown in Table 2.

Each of the remaining questions is to be considered independently, i.e., assume that the only change from the facts given above is the specific change in each individual question.

2. (5 points)F&F is considering adjusting its current mix of customers to include more of its most profitable package, Package B and less of its least profitable package, Package C.Specifically, F&F has a plan to reduce the number of customers for Package C by 15 and increase the number of customers for Package B by 5.(Note that this change will reduce the specialist hours devoted to Package C by 15 x .25 = 3.75 hours and increase the number of specialist hours devoted to Package B by 5 x .75 = 3.75 hours.)

What will be the change in profit as a result of this change in product mix?

3. (5 points) F&F is considering adding another specialist that will work 40 hours per week, thus increasing the number of available specialist hours by 50%.This increase in specialist hours will not be accompanied by any increase in facilities costs of $2,400 per week.

F&F will maintain its current product mix of equal numbers of customers for each of the three packages, so the number of each type of packages will increase from 40 packages of each type to 60 packages of each type.

How much will profit change as a result of this 50% increase in availability of specialist hours?

4. (5 points) F&F is considering adding another specialist that will work 40 hours per week, thus increasing the number of available specialist hours by 50%.This increase in specialist hours will not be accompanied by any increase in facilities costs of $2,400 per week.

F&F plans to devote the additional 40 hours per week of specialist time to whichever type of package will result in the greatest increase in profit.

Which type of package should F&F focus on and how much will profit change as a result of this 50% increase in availability of specialist hours?

5. F&F is considering asking their current specialists to work some overtime hours in order to add some more customers.These additional hours will not be accompanied by any increase in facilities costs of $2,400 per week.F&F will face a 50% premium for overtime, i.e., total employment costs for each specialist overtime hour will be $60 per hour rather than the regular $40 per hour.

a) (3 points)If F&F devotes each overtime hour to whichever type of package will result in the greatest increase in profit, how much will profit change as a result of each overtime hour?

b) (3 points) If F&F devotes each overtime hour to whichever type of package will result in the least increase in profit, how much will profit change as a result of each overtime hour?