Maximize , subject to the constraints
and
and are integers.
Maximize (Z = 5x_1 + x_2 + 3x_3) subject to (-x_1 + 2x_2 + x_3 \le 4), (4x_2 - 3x_3 \le 2), (x_1 - 3x_2 + 2x_3 \le 3), (x_1, x_2, x_3 _________ ______ _________ ___ _____ ______ ___ ______ ________ __________ ____.
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The population dynamics of a species is governed by the discrete model
where r and k are positive constants. Determine the steady states and discuss the stability of the model. Find the value of r at which first bifurcation occurs. Describe qualitatively the behaviours of the population for , where
. Since a species becomes extinct if
for any n > 1, show using iterations, that irrespective of the size of r > 1 the species could become extinct if the carrying capacity
.
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% |
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.
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?
A library wants to improve its service facilities in terms of the waiting time of its borrowers. The library has two counters at present and borrowers arrive according to Poisson distribution with arrival rate 2 every 10 minutes and service time follows exponential distribution with a mean of 15 minutes. The library has relaxed its membership rules and a substantial increase in the number of borrowers is expected. Find the number of additional counters to be provided if the arrival rate is expected to be twice the present value and the average waiting time of the borrower must be limited to half the present value.
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
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 |