Optimization Theory Questions 2022

QUESTION ONE
Indicate if the statements below TRUE or FALSE are and give a DETAILED explanation to
support why it is true or false
1. Optimization theory exemplifies the differentiation of functions. FALSE, functions normally
have a variation in their values.
2. First-order conditions distinguish maximum and minimum turning points. TRUE given that in
any turning points, the initial values have a variation.
3. A maximum in the neighborhood cannot be a global maximum. FALSE because a
maximum within a local function is also within a domain where provided function records a
greater value compared to the neighbors.
4. A positive elasticity means a normal good. TRUE because an increase in income would
automatically results into increase in demand.
5. Optimizing two independent variables, if the determinant of H>0 then results are
indeterminate. TRUE but only H is a positive value.
6. The derivative of a linear function will not necessarily be a constant function. TRUE because a
lineal function derivative is a constant function and, in most cases, dos does not change the
derivative despite moving up and down.
7. A scalar matrix must be a square matrix. TRUE because its diagonal also contains only the
provided scalar while other entries are zero.
8. A singular matrix can be inverted. FALSE because its determinant is zero.
9. Matrices A2x3 and B3x2 are feasible in the order AB and not BA. TRUE because AB is not
equal to BA.
10. The inverse method is a way of obtaining the inverse of a matrix. TRUE because normally
the matrix variable D is solved through left-multiplying both sides of the given matrix equation
(PD=C) by O-1.
[30 marks]
QUESTION TWO
1. Explain three real-life practical applications of Markov analysis, use real business examples.
[10 Marks]
1) Stock speculators- through this process, it is easy for the opportunistic to estimate the
probability that a given stock is likely to outperform other stocks in the market for a
given period of times, (Mohammadi, et, al, 2018).
2) Availability- for instance, the process can identify the feeding system in general like for
the industry of sugar that might have been established to be underperforming so that
through the modelling and numerical analysis in the process can help in obtaining results
for decision making.
3) Obtaining optimal systems for example designing constituents that enhance freedom from
failures during operations for a reasonable period that is key when it comes to maximum
system productivity.
2. Two sales outlets, S and T, compete in the same market. At the beginning of the first week of
the study analysis, there were 12,800 customers distributed equally between the two competitors.
Preliminary analysis indicates that during any week 70% of S’s customers remained loyal while
the rest shifted their loyalty to T. On the other hand, 60% of T’s customers remain loyal during
each week.
Required