U.S. postal rules require that the length plus the girth of a package cannot exceed 84 inches in order to be mailed. Find the exact dimensions of the rectangular package of greatest volume that can be mailed. [Note: From the figure bel we see that 84 = (length) + (girth) = / + (2x + 2y).] nches inches inches 7. [-/6 Points] DETAILS MY NOTES A monopolist manufactures and sells two competing products, call them I and II, that cost $46 and $39 per unit, respectively, to produce. The revenue from marketing x units of product I and y units of product II is R(x, y) = 114x + 131y - 0.04xy - 0.1x2 - 0.2y2. Find the exact values of x and y that maximize the monopolist's profits. X =[ 8. [-/4 Points] DETAILS MY NOTES Given the line y = 2.5x + 3, find the sum of the squared errors (also known as the error sum of squares or the error), E, for the three points (1, 2), (2, 6) and (4, 5). (Give an exact answer. Exact answer means give your answer as a fraction or a terminating decimal, DO NOT round.) E = 9. [-/12 Points] DETAILS MY NOTES In this question, you will find the least-squares line, y = Ax + B through the points (0, -4), (1, 1), (3, 2) and (6, 5). The error (sum of squared errors) is a function of A and B. State this function. (Give an answer in terms of A and B.) We want to find the values of A and B that minimize this function. As usual, we do this by calculating partial derivatives and then solving the simultaneous equations that result from setting both derivatives equal to zero. Calculate the partial derivatives. (Give answers in terms of A and B.) aE aE aB Set both partial derivatives equal to zero. Rearrange the equation - = 0 to give A in terms of B. 4 = Now, substitute the above into the equation - = 0 and solve for B. (Give an exact numerical answer with no variables. Exact answer means give your answer as a fraction or a terminating decimal, DO NOT round.) B = Finally, find the value of A. (Give an exact numerical answer with no variables. Exact answer means give your answer as a fraction or a terminating decimal, DO NOT round.) A = 10. [-/4 Points] DETAILS MY NOTES Consider the following data points. (1, 10) (2, 5) ( 5 , 3 ) Use partial derivatives to obtain the formula for the best least-squares fit to the data points. y (x )