Fancy Florals currently uses one delivery truck for all its deliveries. There is
ID: 3173210 • Letter: F
Question
Fancy Florals currently uses one delivery truck for all its deliveries. There is 2% chance the truck will break down resulting a loss of $6,000 to the company. The company can get can either one or two more trucks and divide its deliveries evenly between the trucks. With two trucks, the probability that each truck will break down is 2% and if one truck breaks down the loss will be $3000. Write three trucks, the probability that each truck will break down is 2% and if one truck breaks down, the loss will be $2000 a) What is the expected loss with one deliver truck? Variance of the expected loss? b) What is the expected loss with two delivery trucks? Variance of the expected loss? c) What is the expected loss with three delivery trucks? Variance of the expected loss? d) Which strategy causes the company to face the most risk? Justify your answer quantitatively.Explanation / Answer
a) Expected loss if one delivery truck = 0.02 * 6000 = $120
(Since chance that the truck will break down is 2% and the corresponding loss will be $6000)
Variance of the expected loss = 0.02 * 60002 = $720000
b) Expected loss if two delivery trucks = 0.02 * 3000 = $60
(Since chance that the truck will break down is 2% and the corresponding loss will be $3000)
Variance of the expected loss = 0.02 * 30002 = $180000
c) Expected loss if three delivery trucks = 0.02 * 2000 = $40
(Since chance that the truck will break down is 2% and the corresponding loss will be $2000)
Variance of the expected loss = 0.02 * 20002 = $80000
d) Probability that one out of three trucks will breakdown is 1/3 = 0.33 (we assume that all 3 trucks are equally likely to breakdown). Similarly probability that one out of 2 trucks will breakdown is 1/2 = 0.5.
So the more trucks we have lesser are the chances of breakdown. Hence the company should have 3 trucks for delivery.
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