Quiz 8 — Capstone (Lectures 29–32)

Time: 20 minutes · Closed book · Answer all questions. This quiz samples the whole course; each question names the lecture that taught the tool.

Q1. Formulation (5 marks)

A student council has 300 and wants to fund as many events as possible. Available events have costs 40, 55, 80, 120, 150, and 190; each event is either funded in full or not at all.

(a) State the objective and the constraint in one sentence each. (2) (b) Give the optimal selection and its objective value. (2) (c) Which lecture's technique solves this at general scale, and why does "cheapest first" work here? (1)

Q2. Expected value (5 marks)

A raffle ticket costs 2. Prizes: one prize of 50 with probability 1/200, ten prizes of 5 with probability 1/20 each (independent of the first question — treat the two prize types as separate, non-overlapping draws).

(a) Compute the expected value of one ticket, showing the calculation. (3) (b) Should a rational player buy, on expected value alone? One sentence. (1) (c) Name one factor outside expected value that could still justify buying. (1)

Q3. Strategy under uncertainty (5 marks)

A data-science team must choose: ship Model A (accurate on historical data, untested on live traffic) or Model B (less accurate on history, but robust in a one-week live pilot).

(a) Frame this as a decision under uncertainty: what are the outcomes and what is unknown? (2) (b) The team can buy one week of live data about Model A before deciding. In one sentence, what is the value of that information? (2) (c) Which lecture's framing is this? (1)

Q4. The 20-minute final (5 marks)

You are handed: "The canteen wants to predict which day next week will sell the most sandwiches, using last month's sales."

(a) Decompose into subproblems (list them). (2) (b) State the two riskiest assumptions. (2) (c) Name the first lecture's rule that (b) exercises. (1)