Hello Please assist with the following set of questions, please provide easy to read solutions [7.5]

1. [-/1 Points] DETAILS BERRAPCALC7 7.5.001.MI. MY NOTES PRACTICE ANOTHER Use Lagrange multipliers to maximize the function f(x, y) subject to the constraint. (The maximum value does exist.) f ( x , y ) = 2xy, x + 2y = 4 Need Help? Read It Watch It Master It Submit Answer 2. [-/1 Points] DETAILS BERRAPCALC7 7.5.009. MY NOTES PRACTICE ANOTHER Use Lagrange multipliers to maximize the function f(x, y) subject to the constraint. (The maximum value does exist.) f ( x, y) = In(xy), x+ y = 2es Need Help? Read It Watch It Submit Answer 3. [-/1 Points] DETAILS BERRAPCALC7 7.5.017. MY NOTES PRACTICE ANOTHER Use Lagrange multipliers to minimize the function f(x, y) subject to the constraint. (The minimum value does exist.) f ( x , y ) = In(x2 + y2), 2x + y = 20 Need Help? Read It Watch It Submit Answer4. [-/1 Points] DETAILS BERRAPCALC7 7.5.019. MY NOTES PRACTICE ANOTHER Use Lagrange multipliers to minimize the function f(x, y) subject to the constraint. (The minimum value does exist.) f ( x, y ) = ex- + y, x+ 2y = 15 Need Help? Read It Submit Answer 5. [-/1 Points] DETAILS BERRAPCALC7 7.5.023.MI. MY NOTES PRACTICE ANOTHER Use Lagrange multipliers to maximize and minimize the function subject to the constraint. (The maximum and minimum values do exist.) f( x, y) = 4x + 2y, 8x2 + y2 = 216 maximum minimum Need Help? Read It Watch It Master It Submit Answer6. [-/1 Points] DETAILS BERRAPCALC7 7.5.035. MY NOTES PRACTICE ANOTHER Solve using Lagrange multipliers. (The state extreme values do exist.) A metal box with a square base is to have a volume of 1215 cubic inches. X X If the top and bottom of the box cost 150 cents per square inch and the sides cost 90 cents per square inch, find the dimensions (in inches) that minimize the cost. [Hint: The cost of the box is the area of each part (top, bottom, and sides) times the cost per square inch for that part. Minimize this subject to the volume constraint. ] length X = in width X = in height y = in Need Help? Read It Submit Answer9. [1/6 Points] DETAILS PREVIOUS ANSWERS BERRAPCALC7 7.5.032. MY NOTES PRACTICE ANOTHER For the Cobb-Douglas production function P and isocost line (budget constraint, in dollars), find the amounts of labor L and capital K that maximize production, and also find the maximum production. Then evaluate and give an interpretation for | | and use it to answer the question. (a) Maximize P = 2000L3/5k2/5 with budget constraint 154 + 320K = 8000. L = K = P= (b) Evaluate and give an interpretation for |2|. Each additional dollar of budget increases v . production by this amount. (c) Approximate the increase in production if the budget is increased by $60. units Need Help? Read It Submit Answer10. [-/3 Points] DETAILS BERRAPCALC7 7.5.034. MY NOTES PRACTICE ANOTHER Solve using Lagrange multipliers. (The stated extreme values do exist.) A company manufactures two products, in quantities x and y. Because of limited materials and capital, the quantities produced must satisfy the equation 2x2 + 5y2 = 40,768. (This curve is called a production possibilities curve.) 100 2x +5 y- = 40,768 80 60 40 20 X 50 100 150 (a) If the company's profit function is P = 4x + 5y dollars, how many of each product should be made to maximize profit? X = y = (b) Find the maximum profit (in dollars). $ Need Help? Read It Submit