Martha and Ken Allen want to sell their house. At the beginning of each day, they receive an offer. We assume that from day to day, the sizes of the offers are independent random variables and that the probability that a given day’s offer is for j dollars is pj . An offer may be accepted during the day it is made or at any later date. For each day the house remains unsold, a maintenance cost of c dollars is incurred. The house must be sold within 30 days. Formulate a dynamic programming recursion that Martha and Ken can use to maximize their expected net profit (selling price - maintenance cost). Assume that the maintenance cost for a day is incurred before the current day’s offer is received and that each offer is for an integer number of dollar
Martha and Ken Allen want to sell their house. At the
beginning of each day, they receive an offer. We assume that
from day to day, the sizes of the offers are independent
random variables and that the probability that a given day’s
offer is for j dollars is pj . An offer may be accepted during
the day it is made or at any later date. For each day the
house remains unsold, a maintenance cost of c dollars is
incurred. The house must be sold within 30 days. Formulate
a dynamic programming recursion that Martha and Ken can
use to maximize their expected net profit (selling price -
maintenance cost). Assume that the maintenance cost for a
day is incurred before the current day’s offer is received and
that each offer is for an integer number of dollars.
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