(3) A team of scientists is due to spend six months in Antarctica carrying out research. One major piece of equipment they will be taking is subject to breakdowns caused by the sudden failure of a particular component. Because a failed component cannot be repaired, the team intend to carry a stock of spare units of the component but it will cost them roughly $3000 for each spare unit they take with them. However, if the equipment breaks down and a spare is not available a new unit will have to be flown in specially and the team will incur a total cost of $4000 for each unit that is delivered in this way. An engineer who will be traveling with the team has estimated that the number of spares that will be required during the six months follows the probability distribution shown below:

Determine the number of spares that the team should carry if their objective is to minimize expected costs.

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No. of spares required 0 1 2 3 Probability 0.2 0.3 0.4 0.1