Assignment: Production & Operations Management

Answer all three Roman numeral questions I, II, III. Note that question II part c is optional

I. The Readylite Company produces a flashlight in which product managers are trying to decide how long a warranty to issue.
If the managers believe the life of the flashlight follows a normal distribution with a mean of 2 years and a standard deviation of .5 years):

a. What percentage of flashlights sold can they anticipate will be returned within the first two years?
b. What percentage of flashlights sold can they anticipate will be returned within two years?
c. What percentage of flashlights sold can they anticipate will be returned between the first year and the third year?

II. The guidance system of a ship has three modules that must all function properly for the system to work. Two of the modules have reliability of .92, the other has a reliability of .99.

a. Compute the reliability of the system.

b. A backup system identical to the first will be added to the ship. The backup will be switched on automatically if the first system fails. Assuming that the switch to the backup works perfectly, what is the reliability of the ship's guidance system now? Show your calculations.

c. This part is not required. Suppose the backup switch is only 91% reliable. What is your new (revised) answer for the question posed in part b. above? Show your calculations.

III. A producer can produce a product at a variable cost per unit of $7. The producer can sell the product for $12 each. If the fixed cost is $68,000

a. How many units must the producer sell to break-even?
b. What is revenue at 20,000 units? What is total cost at 20,000 units?
c. How many units must the producer sell in order to earn a profit of $66,000?