A company manufacturing soft drinks is thinking of expanding its plant capacity so as to meet future demand. The monthly sale for the past 6 years are available. State, giving reasons, the type of modelling you will use to obtain good estimates for future demand so as to help the company make the right decisions. Also state four essentials and four non-essentials for the problem.
The appropriate modelling approach for estimating future demand of soft drinks using six years of monthly sales data is time series modelling. Monthly sales observations are ordered in time and are likely to exhibit components such as trend, seasonality, and random fluctuations. Since soft drink demand commonly shows seasonal patterns due to weather, festivals, and consumption habits, and may also ___ _______ _________ _______ _____ _______ _______ ______ ____.
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Let G(t) be the amount of the glucose in the bloodstream of a patient at time t. Assume that the glucose is infused into the bloodstream at a constant rate of . At the same time, the glucose is converted and removed from the bloodstream at a rate proportional to the amount of the glucose present. If at
then
i) formulate the model.
ii) find g(t) at any time t.
iii) discuss the long term behavior of the model.
Companies considering the purchase of a computer must first assess their future needs in order to determine the proper equipment. A computer scientist collected data from seven similar company sites so that computer hardware requirements for inventory management could be developed. The data collected is as follows:
| Customer Orders (in thousands) | Add-delete items (in thousands) | CPU time (in hours) |
| 123.5 | 2.108 | 141.5 |
| 146.1 | 9.213 | 168.9 |
| 133.9 | 1.905 | 154.8 |
| 128.5 | 0.815 | 146.5 |
| 151.5 | 1.061 | 172.8 |
| 136.2 | 8.603 | 160.1 |
| 92.0 | 1.125 | 108.5 |
Do the stability analysis of the following model formulated to study the effect of toxicant on prey-predator population and interpret the solution.
Where all the variables and constants are same as defined in the system (32)-(35) except for the following
Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?
| Portfolio | Expected return | Standard deviation |
| W | 10% | 25% |
| X | 5% | 7% |
| Y | 17% | 37% |
| Z | 12% | 13% |
A company manufacturing soft drinks is thinking of expanding its plant capacity so as to meet future demand. The monthly sale for the past 6 years are available. State, giving reasons, the type of modelling you will use to obtain good estimates for future demand so as to help the company make the right decisions. Also state four essentials and four non-essentials for the problem.
Let be a portfolio of two securities X and Y. Find the values of w1 and w2 in the following situations:
i) and P is risk free.
ii) and variance P is minimum.
iii) Variance P is minimum and and
.
A tumour is developing from the organ of a human body with concentration with growth and decay control parameters 7.2 and 2.7 respectively. In how many days the size of the tumor will be twice?