Question 2: Outdoor grilling (18 points) Immerse yourself in the pleasures of unique flavor creations and the gratification of outdoor cooking says the salesman of a particular brand of high-end open-air culinary system. The proposition is simply too good, your passion has been ignited, and as visions of lazy Summer afternoons grilling delicious meats and veggies in your backyard with your friends, colleagues, and Advanced Analytics professor, you simply cannot resist purchasing this amazing piece of equipment. And thus, the following homework problem is motivated... As equipment ages, it typically degrades, resulting in rising maintenance costs and decreasing salvage values. These conditions provide ample reasons to periodically replace such equipment. Consider the specific case described above concerning a new gas griller you purchased to host parties at your home during the next five years. The cost of the grill is $7,600. The cost of maintaining such a high-end item per year is significant if you wish to keep it in the best condition as possible (which, of course, you do). Assume the maintenance costs during a year depend on its age at the beginning of the year, as given in Table 4.

To avoid the high maintenance costs associated with an older grill, you may sell the grill on eBay and purchase a new grill. The price you receive on eBay depends on the age of the grill at the time of sale (see Table 4). Assume that at any time, it costs $7,600 to purchase a new grill. The goal is to minimize the net cost (purchasing costs + maintenance costs - money received from eBay) for the next five years. Note: there is no option to simply sell the grill and not replace it: remember, your passion has been ignited and you must grill! Also, to simplify things, you will only make decisions at the beginning of each year.. For instance, when you first purchase the grill, it costs you $7600. You will keep the grill for at least one year, so you would incur $800 of maintenance costs. Now, at the beginning of the second year, you can either decide to keep it for another year (and incur the additional maintenance costs) or sell it on eBay for $5,000 and buy a new grill for $7,600. Then you would need to make the same decision the next year, etc. Formulate this problem as a shortest-path network flow problem and solve.

Table 4: Open-air culinary system costs and resale values Project Age (years) Maintenance costs eBay value 0 800 1 1250 5000 2 2000 4100 3 2900 1500 4 4800 950 5 0 Table 4: Open-air culinary system costs and resale values Project Age (years) Maintenance costs eBay value 0 800 1 1250 5000 2 2000 4100 3 2900 1500 4 4800 950 5 0