1. Jodi wants to lease a new car and start a part time business to give people car rides. She has contacted three automobile dealers for pricing information. Each dealer offered Jodi a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The three dealers provided the details about the monthly lease cost, the mileage allowance, and the cost for additional miles.
Jodi is not sure how many miles she will drive over the next three years for this business but she believes it is reasonable to assume that she will drive 10,000 miles per year, 14,000 miles per year, or 18,000 miles per year. With this assumption, Jodi estimated her total profit for the three lease options. The three lease options and the associated profits for each are given below:
Dealer 10000 Miles 14000 Miles 18000 Miles
A $ 7000 $10500 $13500
B $ 8500 $11500 $11000
C $10000 $ 9500 $ 9800
Determine the optimal decision to lease the car from a dealer and the profit associated with it by using the following decision criteria.
a. Maximax
b. Maximin
c. Equal likelihood
d. Minimax regret criterion.
2. For the problem given in Question 2, the probabilities are given by P(10000 miles) = 0.5, P(14000 miles) = 0.3 and P(18000 miles) = 0.2.
a. Compute the expected value for each decision and select the best one.
b. Compute the expected regret value for each decision and select the best one.
c. Calculate and interpret the expected value of perfect information.
3. A single-server queuing system with an infinite calling population and a first-come, first-served queue discipline has the following arrival and service rates:
λ = 12.1 customers per hour
µ = 14.5 customers per hour
Determine P0, P1, P4, L, Lq, W, Wq, and U.
4. A bank has one drive-up teller. The teller can serve at the rate of 11.5 bank customer in an hour. Customers arrive at the drive-up window on an average every 7.5 minutes. The bank is currently analyzing the possibility of adding a second drive-up window at an annual cost of $15,000. It is assumed that arriving cars would be equally divided between both windows. It is estimated that each minute's reduction in customer waiting time would increase the bank's revenue by $2,000 annually. Should the second drive-up window be installed?
5. Cakes baked by The Charm City Bakery are transported from the ovens to be packaged by one of five wrappers. Each wrapper can wrap an average of 35 cakes per hour. The cakes are brought to the wrappers at the rate of 160 per hour. Assuming it is a multiple-server waiting line model; determine the average number of cakes waiting for a wrapper and the average time a cake must wait for the wrapper. What is the probability that there will be more than 5 cakes in the system?