A gold mine operates in an open pit accessed by means of haul road developed at a gradient of 12° with a total length of approximately 3500m to the bottom of the pit. At the current production level at the bottom of the pit ore and waste are loaded from two identical shovels located at 150m and 250 respectively from the end of the haul road, each shovel can load a truck in a time that is normally distributed with mean 8 minutes and standard deviation of 1 minute.
At the current production level the stripping ratio is 6.4 (SR = Waste/Ore), in consequence you can expect to have 13.5% of the time a truck loaded with ore and 86.5% of the time a truck loaded with waste. The waste dump is located 1800m away from the start of the haul road and the mill is just 700m away from the same point.

In the haul road the trucks will travel at a constant speed following a uniform distribution with range [43,47] Km/h. At the bottom of the pit the speed will be uniformly distributed in the range [25,29] Km/h. Travelling to the mill or waste dump the speed will be normally distributed with mean 50 Km/h and standard deviation of 1.5 Km/h.
It takes exactly 1 minute for a truck to dump in the waste dump or the mill. Each truck costs $450/hour (owning + operating costs).

(i) Manually create a simulation of the first two hours of operations knowing that you have a fleet of 8 identical trucks and initially all of them were queued at the start of the haul road. Determine:
a. The number of truck-loads loaded in two hours
b. The number of truck-loads dumped to both the waste dump and the mill in two hours
c. The total time spent waiting on average in two hours
d. The total time spent travelling on average in two hours
e. The cost of haulage ($/tonne)
(ii) Write a simulation program using EXCEL and VBA to simulate one complete shift with the same initial conditions as before, please note that one shift = 12 hours. The random number generator will be provided by the lecturer. Determine:
a. The number of truck-loads loaded in a shift
b. The number of truck-loads dumped to both the waste dump and the mill in a shift
c. The total time spent waiting on average per truck in a shift
d. The total time spent travelling on average per truck in a shift
e. The cost of haulage ($/tonne)
(iii) Answer the same questions as in part (ii) if the fleet now is 15 trucks

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