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 |
i) Find a linear regression equation that best fit the data.
ii) Estimate the error variance for the regression model obtained in i) above.
Let CPU time (Y) be the dependent variable, customer orders (X_1) and add–delete items (X_2) the independent variables. Using the normal equations for multiple linear regression based on the seven observations, the _____ __________ __________ ___ ________ __________ ____ _______ _______ __________.
__________ _______ _________ __________ ______ _______ _______ ________ ________ _______ ______.
________ ________ _________ _______ ________ _____ _________.
_______ _____ __________ ___ _____ ________ __________ _________ ________.
____ _____ _________ ____ ____ _________.
_____ ________ ________ _____ ____ _______ __________ ___ _________ _____ ________.
_________ ___ _______ _______ ______ _____ ___ _________ ________ _____.
________ _____ _________ _______ _______ __________.
_________ ___ ________ ___ _______ _______ ______ ______.
____ ______ ________ ___ _____ _______ _____ _____ ________.
________ ____ __________ ________ ___ _____ ___.
_________ __________ ____ __________ _____ ____ _______ ________.
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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?
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 |
Consider a discrete model given by
Investigate the linear stability about the positive steady state N by setting . Show that nt satisfies the equation
Hence show that is a bifurcation value and that as
the steady state bifurcates to a periodic solution of period 6.
Do the stability analysis of the following competing species system of equations with diffusion and advection
where V1 and V2 are advection velocities in x direction of the two populations with densities N1 and N2 respectively. a1 is the growth rate, b1 is the predation rate, d1 is the death rate, C1 is the conversion rate. D1 and D2 are diffusion coefficients. The initial and boundary conditions are:
at
and
where are the equilibrium solutions of the given system of equations.
Interpret the solution obtained and also write the limitations of the model.
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
Maximize , subject to the constraints
and
and are integers.
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.