Linear programming model to determine expected mix


Question 1: The Hotel is due to have a refurbishment but rather than follow the current policy of simply replacing furnishings with a similar style you would like to investigate creating three discrete levels of accommodation to pitch specifically at the three clients groups which make up the Hotel's primary markets: business, tourist and special event clients.

You are proposing that 5 of the larger rooms in the 200 room Hotel would be themed for special events such as weddings, birthdays etc. In line with this, you are also proposing an increase in the quality and range of the complimentary products such a fruit bowl, drinks etc and will include butler service for these rooms. The business rooms will also have better quality products than tourist rooms and a business support person.

The Base room cost is for a standard room clean and service but depending on the type of room there will be a difference in other costs. Estimated costs for each of the room types is detailed below along with the budgeted cost limit.

                                     Business    Tourist    Special Event    Available budget
Complimentary products      55           20               65                  5,400
Direct labour                       10           7                 12                 1,550
Base room costs                  50          50                50                10,000
Variable overhead                6            5                  9                  1,100

You have estimated the following prices per night for each of the room types. Due to limits on the number of guests who may access the business lounge at any time, a maximum of 40 business rooms can be sold per night.

                    Business    Tourist    Special Event
Selling Price    $200.00    $160.00    $220.00

Required:

a) Formulate a linear programming model to determine the expected mix of packages to offer to maximise profit, showing all supporting calculations, and solve using a computer package (eg solver in Excel) to derive an optimum accommodation mix.

b) Comment on the solution, was it what you expected? Why or why not?

Question 2: Included in the staff tasks in the ORC is the job to set-up conferences, meetings and other small special events. An analysis of set-up costs indicates a reduction over time where similar corporate events are held which you have attributed to cost experience.

Required:

a) What is meant by the term 'cost experience'?

b) Explain what '80%' refers to when used in the term '80% cost experience curve'.

c) How would you determine the percentage value to apply?

Question 3: Employees of the Hotel are drawn from three categories permanent, part-time and casual. The labour cost has been used as the basis for overhead costs allocation as the overhead costs include a large proportion of human resource. The current method is to calculate overhead cost per dollar of labour cost based on last years cost data using the formula:

(Overhead cost)/(Labour cost) = $0.048 per labour cost dollar.

You have obtained the following data regarding overhead costs and labour activity from the past 12 months.

Month    Number of Employees    Labour Hours    Labour Costs    Overhead Costs
Jan                    70                        32,000            480,000               27,500
Feb                    65                        26,000            390,000               27,000
Mar                    70                        30,000            450,000               30,000
Apr                    75                        42,000            630,000                32,000
May                   80                        45,000             675,000               33,500
June                  87                        55,000             825,000                35,500
July                   92                        65,000             975,000                37,000
Aug                   70                        31,000             465,000                38,500
Sept                  75                        50,000             750,000                37,500
Oct                    75                       45,000              675,000                34,000
Nov                   80                       76,000             1,150,000               38,600
Dec                   80                       65,000               975,000               36,500
                     562,000              8,440,000407,600

You are concerned that this method may not be appropriate and would like to present to the Board of Management a review of the current method.

Required:

a) Plot the data on overhead costs and labour costs?

b) Determine the cost equation for overheads using

i. Labour cost and the following methods

- High-low method
- Regression analysis

ii. Number of employees and the following methods

- High-low method

- Regression analysis

c) Comment on the effectiveness of each method.

d) Based on your findings above how should overhead be allocated, why?

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