1. A shop which sells musical instruments is about to buy some digital pianos, which are much cheaper than traditional acoustic pianos. They can be ordered from the manufacturer at a cost of $1100 each. The selling price will be set at $1325 each. Demand is estimated as being between 12 and 17 inclusive with probabilities 0.2 for 12, 0.3 for 13, 0.2 for 14, 0.15 for 15,0.1 for 16, and 0.05 for 17. After this pur- chase, they expect to see digital pianos with enhanced technology, so any leftover of current stock of digital pianos will be marked down to $700 each (all leftover stock will sell with no problem at this price). All parts (a) to (f) may be done either by hand or by using Excel. (a) In a column give the alternatives, and use a row to give the outcomes. For each alternative and outcome, calculate the possible payoffs. (b) To the right of part (a), create columns to determine a recommendation using each of the following criteria: (i) expected value, (ii) pessimism, (iii) optimism, (iv) Hurwicz using a coefficient of pessimism of 0.6, and (v) Laplace. (c) Verify (b) (i) using the marginal analysis formula. (d) Find the EVPI. (e) Find the payoffs of the regret matrix. (f) Calculate the EOL column, and verify the solution to (d). 1. A shop which sells musical instruments is about to buy some digital pianos, which are much cheaper than traditional acoustic pianos. They can be ordered from the manufacturer at a cost of $1100 each. The selling price will be set at $1325 each. Demand is estimated as being between 12 and 17 inclusive with probabilities 0.2 for 12, 0.3 for 13, 0.2 for 14, 0.15 for 15,0.1 for 16, and 0.05 for 17. After this pur- chase, they expect to see digital pianos with enhanced technology, so any leftover of current stock of digital pianos will be marked down to $700 each (all leftover stock will sell with no problem at this price). All parts (a) to (f) may be done either by hand or by using Excel. (a) In a column give the alternatives, and use a row to give the outcomes. For each alternative and outcome, calculate the possible payoffs. (b) To the right of part (a), create columns to determine a recommendation using each of the following criteria: (i) expected value, (ii) pessimism, (iii) optimism, (iv) Hurwicz using a coefficient of pessimism of 0.6, and (v) Laplace. (c) Verify (b) (i) using the marginal analysis formula. (d) Find the EVPI. (e) Find the payoffs of the regret matrix. (f) Calculate the EOL column, and verify the solution to (d)
