The manager of a Flower Shop promises its customers delivery within four hours on all flower orders. All flowers are purchased on the previous day and delivered to Parker by 8.00 AM the next morning. The daily demand for roses is as follows:
| Dozens of roses | 150 160 170 200 |
| Probability | 0.2 0.3 0.4 0.1 |
The manager purchases roses Rs 50 per dozen and sells them for Rs 150. All unsold roses are donated to a local hospital. How many dozens of roses should Parker order each evening to maximize its profits? What is the optimum expected profit?
Solution Since number of roses (in dozen) purchased is under control of decision-maker, purchase per day is considered as ‘course of action’ (decision choice) and the daily demand of the flowers is uncertain and only known with probability, therefore. it is considered as a ‘state of nature’ (event). From the data, it is clear that the flower shop must not purchase less than 15 or more than 20 dozen roses, per day. Also each dozen roses sold within a day yields a profit of Rs (150 — 50) = Rs 100 and otherwise it is a loss of Rs 50. Thus
Marginal profit (MP) Selling price — Cost = 150 — 50 = Rs 100
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The manager of a Flower Shop promises its customers delivery within four hours on all flower orders. All flowers are purchased on the previous day and delivered to Parker by 8.00 AM the next morning. The daily demand for roses is as follows:
| Dozens of roses | 150 160 170 200 |
| Probability | 0.2 0.3 0.4 0.1 |
In a small town, there are only two stores, ABC and XYZ that handle sundry goods. The total number of customers is equally divided between the two, because price and quality of goods sold are equal. Both stores have good reputation in the community, and they render quality good customer run annual pre-New Year sales during the first week of January. Sales are advertised through a local newspaper, radio and television media. With the aid of an advertising firm store ABC constructed the game matrix given below.(Figures in the matrix represent a gain or loss of customers).
|
| Strategy of XYZ | ||
| Strategy of ABC | Newspaper | Radio | Television |
| Newspaper Radio Television | 30 0 90 | 40 15 20 | – 80 – 20 50 |
A glass manufacturer produces hand mirrors. Each mirror is supposed to meet company standards for such things as glass, color of handle, and so on. To control for these features, the company quality people randomly sample 40 mirrors in every shift and determine how many of the mirrors are out of compliance on at least one feature. Shown here are the data for 15 such samples.
| Sample | Number out of Compliance | Sample | Number out of Compliance |
| 1 2 3 4 5 | 2 0 6 3 1 | 6 7 8 9 10 | 0 4 3 2 2 |
State whether the following statements are True or False. Give reason in support of your answer:
(a) The process capability of a manufacturing process of a certain type of bolt, with mean diameter 2 inches and standard deviation 0.05 inches, will be 0.30
(b) If the probability of accepting a lot of satisfactory quality is 0.9401, then the producer’s risk will be 0.9401.
(c) Hurwicz criterion is a method to solve the problems that involve decision-making under certainty.
(d) Two independent components of a system are connected in series. If the reliability of these components are 0.8 and 0.6 respectively, then the reliability of the system will be 0.92.
(e) For a two person zero sum game, the payoff matrix is given below:
|
| Player B | |||||
| B1 | B2 | B3 | B4 | B5 | ||
|
Player A | A1 | 3 | 4 | 5 | –2 | 3 |
| A2 | 1 | 6 | –3 | 3 | 7 | |
The system shown below is made up of ten components. Components 2, 3 and 4 are not identical and at least two component of this group must be available for system success.
What is the system reliability if R1 = R5 = 0.85, R6 = R7 = R8 = 0.80
, R9 = R10 = 0.70 R2 = 0.40, R3 = 0.50 and R4 = 0.60.
A process of manufacturing an item is in statistical control with
= 250 and
= 3.5.
The specification limits of the process are 200 ± 8 1.90. Calculate the process capability. Does it appear that the manufacturing process is capable of meeting the specification requirements? (d2 = 2.059)
A system having Weibull failure distribution with pdf as
i) Compute the reliability function of the system,
ii) find the reliability for a 100 days mission for θ = 2,
iii) show that the hazard rate is constant,
iv) find the MTTF, and
v) what is the life of the system if reliability of 0.90 is desired.