Question

Jose, the IT manager of the company is responsible to maintain a server for the company’s computer network that would store all of the company’s private information and allows different departments to properly communicate. Jose would like to keep the server most up to date so to prevent any malicious attacks to the IT systems of the company and facilitate information sharing within the company. Therefore, he has decided to replace the server at least every two years.

He has just signed a lease contract with a supplier to get a new server for the company. Under the contract, Jose has made an initial payment of $70,000 to obtain the new server, and would have to pay in subsequent years to replace the server. The contract covers 5 years and the server will be traded in for refund at the end of the 5th year. Under the contract, the price to acquire a new server would increase by 5% every year compared to the year before. But he would be given a trade-in credit of 60% of the purchased price (price at the time of purchase) for any server that is one year old and 40% of the purchased price for any server that is two years old. For example, if the server is purchased in year 2 and was replaced in year 4, the trade-in value will be 40% of year 2 price. Jose has realized that his initial payment is a sunk cost now, but he would like to know when he should replace his equipment in order to minimize the remaining leasing costs over the next five years.

Jose has realized that he can solve this problem using a network model. The following is the network he is thinking about. Each of the nodes 1 – 5 represents the beginning of each of the years that Jose can receive a new server. The “terminate contract” node represents the end of the contract at the end of the 5th year. Each arc in this network represents a choice available to Jose for replacement. For example, the arc from node 1 to node 3 suggests the option that Jose keep the server he initially acquires over the years 1 and 2 and replace it with a new server at the beginning of year 3. The arc from node 2 to node 3 also means that if Jose makes a replacement at the beginning of year 2, he will keep it over the year and replace it with a newer server at the beginning of year 3.

Terminate contract 2

Obtain the price of getting a new server at the beginning of each of the years. Calculate all the costs for all the arcs - note that at the termination of the contract no new server is purchased and the existing server is returned for a credit. Now formulate the problem as a network problem and answer the following questions. Answer all question in the fields provided. For all numerical questions, enter them to within two decimal places, after properly rounding the final answer. If your calculations involve multiple steps, do not round intermediate numbers, round ONLY the final answer.

1 What is the cost for the arc from node 5 to node “terminate contract”?

2 What is the minimum cost of the lease (additional to the initial payment of $70,000)?

3 What is the least amount of capacity that can be set for the arc from node 1 to node 2?

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