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Posted: September 10th, 2021
Assignment: I need help writing a research paper., Dun-Rite Auto services, services suspensions. Customers pay $45 per mechanic hour for suspension work
Q3. Dun-Rite Auto services, services suspensions. Customers pay $45 per mechanic hour for suspension work.
Dun-Rite pays its mechanics a wage of $30 per hour.
However, at the beginning of each day, before it knows the day’s demand, Dun-Rite must commit to paying the mechanics for a contracted number of hours. If demand is higher than planned for, the excess demand must be turned away.
Daily suspension demand is: 40 hours with probability 0.4; 60 hours with probability 0.6.
A. Construct a payoff table and determine the optimal number of hours Dun-Rite should contract for daily with its mechanics?
Assume risk neutrality.
You need to consider only two choices – contract for 40 hours or alternatively 60 hours (there is a mathematical theorem which we will discuss in class later that shows that choices in between, such as contract for 45 or 50 or 55 hours, cannot be optimal).
Demand Scenario : probability Expected payoff
40 hours 0.4 60 hours 0.6
Decision Contract 40 hours
Contract 60 hours
Dun-Rite should contract for __________________ hrs daily.
B. Dun-Rite has observed that suspension demand is correlated with the early morning weather forecast on the local TV station – perhaps the forecast influences customers deciding whether to step out to have their car serviced.
Dun-Rite has also observed that the forecast is either Sunny (FS) or Cloudy (FC) and that
Prob (FS) = 0.2 ; Prob (FC) = _____ ?
Further, Dun-Rite has observed that the combination of 40 hours demand and sunny forecast never occurs.
That is, Prob (Demand = 40 hours & FS) = 0;
Required: Fill up the joint probability table and then compute the posterior probabilities of demand below:
FS FC marginal (unconditional) prob. of demand
Demand 40 hrs
Demand 60 hrs
marginal (unconditional) prob. of forecast
Posterior probabilities:
Pr (40 | FS) = ______________________________ Pr (60 | FS) = ______________________________
Pr (40 | FC) = ______________________________ Pr (60 | FC) = ______________________________
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