Hi I need help please 5,7,10

5. [l1 Points] DETAILS WANEFMAC7 15.4.012. MY NOTES ASK YOUR TEACHER Use Lagrange multipliers to solve the given optimization problem. Find the minimum value of x, y} = x2 + y2 subject to xy2 = 16. Also nd the corresponding points (x, y). (X. y) = ( I ) (smaller y-value) (X. l') = ( I ) (larger y-value) Need Help? 6. [1!1 Points] DETAILS PREVIOUS ANSWERS WANEFMAC? 15.4.021. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the method of Lagrange multipliers to solve this exercise. I want to fence in a rectangular vegetable patch. The fencing for the east and west sides costs $6 per foot, and the fencing for the north and south sides costs only $3 per foot. I have a budget of $144 for the project. What Is the largest area I can enclose? .2 Need Help? 7. [l1 Points] DETAILS WANEFMAC7 15.4.024. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the method of Lagrange multipliers to solve this exercise. Hercules Films is also deciding on the price of the video release of its lm Bride of the Son of Frankenstein. Again, marketing estimates that at a price of p dollars it can sell q = 396,000 18,000}: copies. but each copy costs $4 to make. What price will give the greatest prot? 10. [0.6611 Points] DETAILS PREVIOUS ANSWERS WANEFMAC? 15.4.039.Ml. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The Gym Shirt Company manufactures cotton socks. Production is partially automated through the use of robots. Daily operating costs amount to $180 per laborer and $80 per robot. The number of pairs of socks the company can manufacture in a day is given by a Cobb-Douglas production formula q = 50...10.E|r0.4-Jr where d Is the number of pairs of socks that can be manufactured by n laborers and r robots. Assuming that the company has a daily operating budget of $1,200 and wishes to maximize productivity, how many laborers and how many robots should it use? What Is the productivity at these levels? number of laborers C] [:1 number of robots What is the productivity at these levels? HINT [See Example 5.] (Round your answer to the nearest pair of socks.) x pairs of socks per day