IE $301$ Fall $2019$Sample Questions for Midterm $-2$ INSTRUCTIONS $$Anything we talked about dynamic programming $($both deterministic and probabilistic$)$ in class might show up on your exam. Just because a topic is not covered in these questions does not mean that I will not test you on it$.$This exam is longer than the test you will have, but I think this way, you have more questions to practice. $$You will NOT be allowed to use and refer to the book, notes, handouts, homework solutions or any other resources in the test. $$You will be allowed to use a calculator, but you cannot share it with a friend. Cell phone calculators are NOT allowed. In all of the following questions, make sure you write the stages, states, decisions and the recursive relationship clearly. Question $1$ An electronics firm has a contract to deliver the following number of radios during the next three months; month $1,200$ radios; month $2,300$ radios; month $3,300$ radios. For each radio produced during months $1$ and $2,$ a $$10$ variable cost is incurred; for each radio produced during month $3,$ a $$12$ variable cost is incurred. The inventory cost is $$1\mathrm{.}50$ for each radio in stock at the end of a month. The cost of setting up for production during a month is $$250.$ Radios made during a month may be used to meet demand for that month or any future month. Assume that production during each month must be a multiple of $100.$ Given that the initial inventory level is $0$ units, use dynamic programming to determine an optimal production schedule