Please if you can help do most of these questions I am stuck and don't know how to solve them.

4. Find the points on the ellipsoid 4x2 + 2y2 +3= = 6 where the tangent plane is parallel to the plane 2x + 4y + 6z = 7. Sketch the ellipsoid and identify the points you found. 7. You have been tasked to build a rectangular box. The top and bottom are to be built out of 2 cm thick aluminum. The density of aluminum is 2.7 g per cms, and the cost $6 per kg. The front and back walls are to be build out of 1 cm thick stainless steel. The density of stainless steel is 7.5 g per cm", and the cost $4 per kg. Finally, the 2 remaining walls are to be built out of 1 cm thick copper. The density of copper is 9.0 g per cm", and the cost $9 per kg. Find the measurements and total price of the least expensive such box that has volume 1 m3. 8. Find the extreme values for the function ry + yz subject to the two constraints ry = 1 and y- + 22 - 1 = 0. Hint: this may be easier than it seems