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- The probability that the majority of a three- person jury will convict a guilty person is given by the formula:P(r, s, t) = rs(1 - t) + (1 - r)st + r(1 - s)t + rst subject to the constraint thatr + s + t = a,where r, s, and t represent each of the three jury members’ probability of reaching a guilty verdict and a is some fixed constant that is generally less than or equal to the number of jurors. Source: Mathematical Social Sciences.(a) Form the Lagrange function.(b) Find the values of r, s, and t that maximize the probability of convicting a guilty person when a = 0.75.(c) Find the values of r, s, and t that maximize the probability of convicting a guilty person when a = 3.Market research indicates that consumers will buy x thousands of units of a particular kind of coffee markers when the unit price is: p(x)=-0.27x + 51 dollars. The cost of producing the x thousands units is C(x)=2.23x^2 + 3.5x +85 A. How much revenues R(x) and profit P(x) are obtained from producing x thousands of units (coffee markers)? B. For what values of x is production of the coffee marker profitable? Note: For part b of this question, please provide a detailed explanation and show your workA study shows that the fewer the number of wolves in a rural area (Y), the more farms there are in the area (Y).A classmate argues that the number of farms should be limited because it is damaging the wolf population. Howwould you respond to that conclusion?
