4. II'_'.onsider the following optimization problem: It is desired to know the dimensions of a rectangular box without a lid of minimum area, which has a cach of 32 1:113 If it is assumed that 3:, 3r are the dimensions of the base of the box and h is the height,r then the above problem can be solved by optimizing the following objective function: 123:2 + 541 + $43,- A: Aim): my Iy+32r+32y B Ax, = J l 3;] my Iy+4r+4y G Ax, = II ( 3;} my I2y2+3x+32y DJ Alias] = I?! 8. Consider the solid Q bounded by the surface of equation y = x- + z and the plans y = 4, 2V3 = x, z = 0, like shown in the next figure: Q Select the integral that allows you to calculate the volume of the solid Q. A) V = J J. J. rayarde DJ V = JJJ rdyarde9. Consider the double integral dA where R is the region of the XY plane, given in the attached graph. (a + 1) + (y-1)' =2 R. c'ty=4 When transforming the previous integral applying change of variable in polar coordinates, we obtain cos 0 drde r cos 0 drde DJ 1 = [" ." coso drab + cos0 drdl