Country : South Africa
Assignment Task:

Task:

Question 1 (20 marks)
The Only One is a boutique hotel that is operated on the KwaZulu-Natal north coast. Currently the hotel consists of 56 Gold class rooms of 50m 2 each, and 16 Platinum class rooms of 75m 2 each. Gold rooms are currently priced at R2250 per person per day for single occupancy and at that price the daily demand is normally distributed with a mean of 40 rooms and a standard deviation of 8. For double occupancy they offer a discount of 10% on the single occupancy rates. The Platinum rooms are priced at R5500 per room per day, irrespective of whether there are one or two guests in the room. The demand for these rooms is very variable – it can be approximated by a uniform distribution with a minimum of zero and a maximum of 25 rooms daily.
From past records they have established that 15% of the Gold rooms sold were for single occupancy and the rest were sold for double occupancy.
Prior to the peak summer season, the owners of The Only One are considering revamping the hotel a little, especially by converting a number of the Platinum rooms to Gold rooms or vice versa. Since they do not want to add to the building, they can convert 2 Platinum rooms to 3 Gold rooms (both requiring a combined 150m 2 of floor space) in multiples of 2 Platinum rooms (or vice versa – 3 Gold rooms converted into 2 Platinum rooms).

 

Use the data in the sheet named “OnlyOne” and build a simulation model that will assist the owners of The Only One with the revamping decision. Simulate the daily revenue from the operations of the hotel in steps of 2 Platinum rooms. From the simulation results compute the average daily revenue as well as the standard deviation of this daily revenue. In addition, determine the probability of generating at least R150 000 revenue daily for each of the simulated room combinations. Also determine the probability that any room that is available on a particular day will end up as unoccupied.
Advise the owners of The Only One on the number of Platinum rooms and supply a motivation for your answer.

 

Question 2 (20 marks)
The Kirkwood Farmers’ Cooperative (KFC) in the Eastern Cape receives oranges from their members. They then sell the oranges in the export market on behalf of their members or they produce orange juice which they sell on behalf of their members. The cooperative has committed to the farmers to buy their full crop at R8 per kg.

Oranges that they receive are graded according to a numeric scale from 1 (poor) to 10 (excellent). The current crop consists of 50 000 kg of Grade 4 oranges, 130 000kg of Grade 6 oranges and 120 000 kg Grade 9 oranges. The quality of oranges sold as fresh fruit for the export market needs to be at least Grade 8 (no blending), while the average quality of the fruit used for juice must be at least of Grade 7. Assume that the oranges of different grades may be blended to produce juice of suitable quality. For example, 1 kg Grade 9 oranges and 2 kg Grade 6 orange have a combined grade point of 9 +2*6 = 21, which is on average 21/3 = 7 and hence satisfies the juice requirement.

The selling price of the juice is R20 per kg of fresh fruit equivalent, while the fresh fruit for export realises R18 per kg. Production costs for the juice amounts to R4.50 per kg of fresh fruit, while the fresh fruit for export incurs a packaging cost of R0.50 per kg.

The maximum demand for juice is the equivalent of 150 000 kg of fresh fruit, while the export orange market will not take more than 100 000 kg. Up to 40 000 kg of oranges can be supplied to the Addo Elephant Park as animal feed at a selling price of R3 per kg.

The operations manager of the cooperative would like to know how to use the crop to maximise profit. The data was capture and used to build a linear programming model that maximised profit. A screen print of the model as well as that of the Answer and Sensitivity reports are attached.

 

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  • Uploaded By : Pearl
  • Posted on : January 20th, 2019
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