Q1. A specialty software development firm is planning to offer one of four new software products and wishes to maximize profit, minimize risk, and increase market share. If a weight of 65% is assigned to profit potential, 20% to profitability risk, and 15% to market share, identify the product that would be best for the firm to introduce.
|
New product
|
Profit potential ($)
|
Profit risk ($)
|
Market share
|
|
SW1
|
80k
|
40k
|
High
|
|
SW2
|
120k
|
30k
|
Low
|
|
SW3
|
160k
|
60k
|
Medium
|
|
SW4
|
120k
|
40k
|
Medium
|
Q2. The following payoff matrix indicates the expected profits associated with three decision options and three states of nature:
|
|
State of nature
|
|
S1
|
S2
|
S3
|
|
Option
|
T1
|
30
|
50
|
60
|
|
T2
|
40
|
60
|
20
|
|
T3
|
60
|
20
|
40
|
Select the decision option that should be selected for i) the maximin rule, ii) the maximax rule, iii) the Laplace rule, iv) the Hurwicz rule with α=0.25.
Q3. An item of energy-efficient equipment can be installed for $20,000, and which is expected to have a salvage value of $5,000 after 20 years, is expected to save $8,000 in energy costs per year.
i) What is the rate of return if the equipment is in operation for 20 years?
ii) For what lifetime will the equipment give a return of 10% ?
Q4. A manufacturing plant has the capacity to assemble 500,000 units per year. At present it is operating at 75% of capacity. The annual income is $500,000. The annual fixed cost is $150,000 and the variable cost $0.40 per unit assembled.
i) What is the annual profit or loss of the centre?
ii) At what volume of output does the centre break even?
iii) What will be the profit or loss at 70%, 80% and 90% of capacity on the basis of constant income per unit and constant variable cost per unit?
Q5. A used automobile can be purchased by a student to provide transportation to and from university for $10,000 as-is (i.e. without warranty). First year maintenance cost is expected to be $400 and the maintenance costs will increase by $100 per year thereafter. Operation costs for the automobile will be
$2,000 for every year the automobile is used and its salvage value decreases by 15% per year.
i) What is the economic life of the vehicle without considering the varying value of money over time?
ii) What is the economic life of the vehicle if the rate of interest is 5%?
Q6. A component manufacturer has a demand of 160 units per week. No shortages are allowed. It costs $250 to initiate manufacturing to produce at a rate of 500 units per week. The unit production cost is $40. The holding cost is $0.25 per unit. Determine
i) the minimum cost production quantity,
ii) the minimum cost procurement level if production lead time is 12 weeks.
Q7. Customers arrive at a rate of 180 per hour at either of two vending machines, each of which can service 240 customers per hour. Assuming a Poisson distribution for arrivals and an exponential distribution for the service time, determine the expected waiting time per customer. Recalculate if one of the vending machines is broken and cannot be used.
Q8. In Question 7 above, if the cost of operating a vending machine over its lifetime is $100 per day, and the cost of having customers waiting for service is 50 cents per minute, what is the optimum number of vending machines?
Q9. A survey taken over 20 days showed the number of defective cars on a highway as per Table I, below. A sample of 150 cars was taken during each day. Construct a c-chart for the data. Is there any assignable cause of variation during this period?
|
Day
|
Defective cars
|
Day
|
Defective cars
|
|
1
|
12
|
11
|
9
|
|
2
|
15
|
12
|
7
|
|
3
|
13
|
13
|
13
|
|
4
|
7
|
14
|
10
|
|
5
|
14
|
15
|
6
|
|
6
|
17
|
16
|
18
|
|
7
|
8
|
17
|
15
|
|
8
|
21
|
18
|
5
|
|
9
|
12
|
19
|
14
|
|
10
|
14
|
20
|
12
|
Q10. Eight maintenance activities, their normal durations in weeks, and the crew sizes for the normal conditions are as follows:
|
Activity
|
Duration (weeks)
|
Crew size
|
|
AC
|
4
|
6
|
|
BC
|
6
|
8
|
|
BE
|
3
|
3
|
|
CD
|
2
|
3
|
|
CE
|
4
|
2
|
|
DF
|
6
|
4
|
|
EF
|
5
|
5
|
|
FG
|
4
|
8
|
i) Represent the maintenance project in the form of an activity-event network.
ii) Identify the critical path and find the minimum time for project completion.
iii) Extra crew members can be used to expedite activities BC, DF and EF at a cost given below:
|
Extra crew
|
Weeks saved
|
Crash cost per week
|
|
1
|
1
|
$100
|
|
2
|
2
|
$125
|
|
3
|
2
|
$150
|
|
4
|
3
|
$200
|
If there is a penalty cost of $1,200 per week beyond the minimum maintenance time of 16 weeks, then recommend the minimum-cost schedule.