A restaurant produces fresh burgers for its customers every day. The company is known for supplying fresh burgers and never uses burgers prepared on the previous day. Demand for burgers is uncertain, preparation capacity is limited, and the restaurant has the option of producing 0, 100, 200, 300 and 400 burgers every day. It has been estimated that the cost of producing each burgers pack is Rs.15. Each burger is sold for Rs. 20. Prepare a payoff matrix when 0, 100, 200, 300 or 400 demands of the burgers turn up on any given day. Prepare an opportunity loss table and hence find the optimum strategy.
To prepare a payoff matrix and find the optimum strategy in this scenario, we need to consider the various combinations of production levels and demand scenarios. Let's create a payoff matrix and then calculate the opportunity loss table.
Payoff Matrix:
The rows represent the production levels (0, 100, 200, 300, 400), and the columns represent the demand scenarios (0, 100, 200, 300, 400). The payoff is calculated as the profit (revenue - cost) for each combination.
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The department of transportation has mandated that the average speed of cars no interstate highways be no more than 70 km per hours in order. To check that the people follow it or not, a researcher took a random sample of 186 cars and found that the average speed was 68 km per hours with a standard deviation 0.6 km per hours.
(a) Find the standard error of the mean
(b) Construct the interval around the sample mean that would contain the population mean 95% of the time.
(c) If the researcher wants to test that the true mean speed on its highways is 70 km per hours or less with 95% confidence then
(i) State null and alternative hypotheses
(ii) Name the test which is suitable in this situation and why?
(iii)Calculate the value of test statistic and critical value.
(iv)Draw the conclusion on the basis of the applied test.
The annual sales revenue (in lakhs of Rs) of a product as a function of sales force (number of salesmen) and annual adverting expenditure (in Thousands of Rs) for the past 10 years are summarised in following table:
| Annual Sales Revenue Y(in Lakhs) | Sales Force X1 (in Number) | Annual Advertising Expenditure X2 (in Thousand) |
| 100
115
125
135
105
145
110
120
135
175 | 40
65
40
90
115
80
50
60
70
100 | 140
115
190
80
100
140
115
150
130
160 |
An urn contains 10 white marbles, 15 blue marbles, and 20 red marbles. Five marbles are selected, one at a time, with replacement. Find the probability that at least one color will be missing from the 10 selected marbles
If the coefficient of determination is 0.833, the number of observations and independent variables are 12 and 3, respectively, then Adjusted R2 will be 0.84.
If the probability density function of a random variable X follows F-distribution is
then degrees of freedom of the distribution will be (2,2).
The following data is the data pertaining to a feeding trial on sheep. Treatments
A: Grazing only
B: Grazing + Maize Supplements
C: Grazing + Maize + Protein Supplement P1
D: Grazing + Maize + Protein Supplement P2
E: Grazing + Maize + Protein Supplement P3
Layout and Wool Yield (100 gm) is given as:
| 32 (D) | 33 (E) | 30 (C) | 28 (B) | 24 (A) |
| 51 (C) | 45 (D) | 41 (A) | 45 (E) | 29 (B) |
| 41 (E) | 29 (A) | 24 (B) | 36 (D) | 35 (C) |
| 38 (B) | 39 (C) | 42 (E) | 23 (A) | 37 (D) |
| 38 (B) | 24 (B) | 21 (D) | 29 (C) | 26 (E) |
For the following Auto regressive model
Xt = 0.7Xt-1- 0.4Xt-2 + at