Consider the cubic total cost function
Assume that the price of q is 15 per unit. Find the output which yields maximum profit.
b) Apply dominance to find the optimum strategies of A and B from the pay-off matrix given below
| Player B | |||
| u | v | ||
| x |
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| |
| Player A | y |
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| z |
|
| |
c) Suppose that the previous forecast was 2090 and the actual value of the variable of interest for the period was 1985 and the oldest value of interest was 1955. Using the moving average technique based upon the most recent four observations find new forecast for the next period.
The total revenue is (R = 15q). Hence profit is (\pi = R - C = 15q - (0.06q^{3} - 0.8q^{2} + 13q + 10) = -0.06q^{3} + 0.8q^{2} + 2q - 10). For maximum profit, (\dfrac{d\pi}{dq} = -0.18q^{2} + 1.6q + 2 = 0). Multiplying by 100 gives ( -18q^{2} + 160q + 200 = 0), or _______ _____ _________ ___ ____ ________.
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एक प्रक्षेप्य को दो अलग-अलग प्रक्षेप कोणों और
पर एक अचर चाल v से इस तरह नियत कर दिया गया कि इससे समान परास प्राप्त हो। दिखाइए कि
दिए हुए प्रतिभूति समुच्चय में उनकी सभी निवेश सूचियां प्रदेश की परिसीमा पर या उसके अंदर स्थित है जैसा कि चित्र 1 में दिखाया गया है।
सुसंगत प्रदेश में वह निवेश सूची ज्ञात कीजिए जिसका अधिकतम प्रतिफल हो। इस प्रदेश में वह निवेश सूची भी ज्ञात कीजिए जिसमें न्यूनतम जोखिम हो।
ख) सुसंगत प्रदेश के दक्ष सीमांत को चित्रित करने की विधि की व्याख्या कीजिए।
ग) यदि n प्रतिभूतियों की सभी निवेशसूचियां प्राप्त हो तो एक उत्तम निवेश सूची का चयन करने के लिए निवेशक को कौन-सा निकस अपनाना चाहिए।
State two real-world problems where you think that mathematical modelling is the only approach to find the solution of the problem. Give 4 essentials for each of the problems. Why do you think that there is no other scientific alternative for the treatment of these problems.
b) Classify the following into linear and non-linear models, justifying your classification.
i) Simple harmonic motion for small amplitude of oscillation.
ii) Population growth model given by
iii) Equation for velocity v of a particle at any time t, moving with a constant acceleration a, and initial velocity u.
iv) Equation describing dynamic stability of market equilibrium price given by
$
and pt is the price in period t.
For a given set of securities, all their portfolios lie on or within the boundary of the region shown in Fig.1.
In the feasible region, find a portfolio which has maximum return. Also, find a portfolio in this region which has minimum risk.
b) Explain the method of delineating the efficient frontier of a feasible region.
c) Given all the portfolios of n securities what criterion would an investor use to select a good portfolio?
Consider the group of individuals born in a given year () and let n(t) be the number of these individuals surviving t year later. Let x(t) be the number of members of this group who have not had smallpox by year t and are therefore still susceptible. Let
be the rate at which susceptibles contract smallpox and let v be the rate at which people who contract smallpox die from the disease. Finally, let
be the death rate from all causes other than smallpox. If dx / dt and dn / dt are, respectively the rates at which the number of susceptibles and entire population decline due to contraction from smallpox and also due to death from all causes then
i) Formulate the above problem by writing equations for dx / dt and dn / dt.
ii) Taking , show that z satisfies the initial value problem
iii) Find z(t) at any time t.
iv) Bernoulli estimated that . Using these values, determine the proportion of 20 years old who have not had smallpox.
अपने वर्गीकरण की पुष्टि करते हुए निम्नलिखित को रैखिक और अरैखिक निदर्शों में वर्गीकृत कीजिए
I) लघुदोलन आयाम वाली सरल आवर्त गति
III) किसी समय पर अचर त्वरण और प्रारंभिक वेग यू से गतिमान एक कण के वेग का समीकरण
एक ट्यूमर पर रसायन औषधि के प्रभाव जबकि इन्हें एक दी हुई अवधि तक रोगी को दिया गया हो।