A two-person zero-sum game having the following payoff matrix for player A
(i) Check whether saddle point exit or not.
(ii) If saddle point does not exit then determine optimal strategies for both the manufacturers and value of the game.
### Understanding the Problem We are given a two-person zero-sum game with a specific payoff matrix for Player A. The tasks are: 1. Check for the existence of a saddle point. 2. If no saddle point exists, determine the optimal strategies for both players and the value of the game. First, let's recall some key concepts: - Zero-sum game: A game where one player's gain is the other player's loss. The sum of the payoffs is zero. - Payoff matrix: A matrix that shows the payoffs for each combination of strategies chosen by the players. - Saddle point: A point in the payoff matrix that is the minimum in its row and the maximum in its column. If a saddle point exists, it represents the value of the game, and the corresponding strategies are optimal for both players. ### Step 1: Representing the Payoff Matrix The problem provides a payoff matrix for Player A, but it's embedded in an image. Since I can't view images, I'll assume a generic 2x2 payoff matrix for illustration. Let's define the matrix as follows: ``` Player B Strategy 1 | Strategy 2 Player __________ ___ ___ _________ ____ _______ ____ __________ _________ __________ ___.
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An office supply company ordered a lot of 400 printers. When the lot arrives the company inspector will randomly inspect 12 printers. If more than three printers in the sample are non-conforming, the lot will be rejected. If fewer than two printers are non-conforming the lot will be accepted. Otherwise, a second sample of size 5 will be taken. Suppose the inspector finds two non-conforming printers in the first sample and two in the second saraple. Also AQI. and LTPD at 0.05 and 0.10 respectively. Let incoming quality be 4%
i) What is the probability of accepting the lot at the first sample?
ii) What is the probability of accepting the lot at the second sample?
iii) Find AQL and ATI
A manufacturer of men's jeans purchases zippers in lots of 500. The jeans manufacturer uses single-sample acceptance sampling with a sample size of 10 to determine whether to accept the lot. The manufacturer uses 2 as the acceptance nuraber. Suppose 3% nonconforming zippers are acceptable to the manufacturer and 8% oncoming zippers are not acceptable. Let incoming quality be 4%
i) Construct an OC carve
ii) Average outing quality (AOQ), if the rejected lots are scromed and all defective zippers are replaced by non-defectives
i) Average total inspection (ATI).
The failure data for 40 electronic components is shown below:
| Operating Time (in hours) | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 |
| Number of Failures | 5 | 7 | 6 | 4 | 5 | 4 |
| Operating Time (in hours) | 30-35 | 35-40 | 40-45 | 45-50 | ≥50 | |
| Number of Failures | 4 | 0 | 2 | 1 | 2 |
At a call omtre, callers have to wait till an operator is ready to take their call. To monitor this process, 5 calls were recorded every hour for the S-hour working day. The data below shows the waiting time in seconds:
| Time | Sample Number | ||||
| 1 | 2 | 3 | 4 | 5 | |
| 9 a.m | 8 | 9 | 15 | 4 | 11 |
| 10 | 7 | 10 | 7 | 6 | 8 |
| 11 | 11 | 12 | 10 | 9 | 10 |
| 12 | 12 | 8 | 6 | 9 | 12 |
| 1 p.m. | 11 | 10 | 6 | 14 | 11 |
| 2 | 7 | 7 | 10 | 4 | 11 |
| 3 | 10 | 7 | 4 | 10 | 10 |
| 4 | 8 | 11 | 11 | 11 | 7 |
Twenty saraples each of size 10 were inspected. The number of defectives detected in cach of them is given below: : 0, 1, 0, 3, 9, 2, 0, 7, 0, 1, 1, 0, 0, 3, 1, 0, 0, 2, 1, 0 Find the control limits for the number of defectives and establish quality standards for the future. Plot the graph and interpost.
A system has seven independent components and reliability block diagram of it shown blow:
Find reliability of the system.
A two-person zero-sum game having the following payoff matrix for player A
(i) Check whether saddle point exit or not.
(ii) If saddle point does not exit then determine optimal strategies for both the manufacturers and value of the game.