4. -/0.43 pointsHHCalc6 15.3.004. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. (If an answer does not exist, enter DNE.) f(x, y) = x3 + y, 3x2 + y2 = 4 maximum minimum 5. -/0.43 pointsHHCalc6 15.3.006. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. (If an answer does not exist, enter DNE.) f(x, y) = 2xy, 5x + 4y = 100, maximum minimum 6. -/0.43 pointsHHCalc6 15.3.007. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. (If an answer does not exist, enter DNE.) f(x1, x2) = x12 + x22, maximum minimum x1 + x2 = 9 7. -/0.43 pointsHHCalc6 15.3.008. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. (If an answer does not exist, enter DNE.) f(x, y) = x2 + y, x2 y2 = 1 maximum minimum 8. -/0.43 pointsHHCalc6 15.3.009. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. (If an answer does not exist, enter DNE.) f(x, y, z) = x + 9y + 3z, x2 + y2 + z2 = 1 maximum minimum 9. -/0.43 pointsHHCalc6 15.3.010. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. (If an answer does not exist, enter DNE.) f(x, y, z) = x2 y2 12z, maximum minimum x2 + y2 = 4z 10.-/0.43 pointsHHCalc6 15.3.011. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. (If an answer does not exist, enter DNE.) f(x, y, z) = xyz, x2 + y2 + 4z2 = 12 maximum minimum 11.-/0.43 pointsHHCalc6 15.3.012. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. (If an answer does not exist, enter DNE.) f(x, y) = x2 + 2y2, x2 + y2 4 maximum minimum 12.-/0.43 pointsHHCalc6 15.3.013. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. (If an answer does not exist, enter DNE.) f(x, y) = x + 3y, maximum minimum x2 + y2 2, 13.-/0.43 pointsHHCalc6 15.3.015. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. (If an answer does not exist, enter DNE.) f(x, y) = x3 + y, x+y1 maximum minimum 14.-/0.43 pointsHHCalc6 15.3.016. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. (If an answer does not exist, enter DNE.) f(x, y) = (x + 7)2 + (y 7)2, x2 + y2 32 maximum minimum 15.-/0.43 pointsHHCalc6 15.3.017. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. (If an answer does not exist, enter DNE.) f(x, y) = x2y + 3y2 y, maximum minimum x2 + y2 10 The Lagrange multiplier is approximately equal to the change in C(x, y) given a five unit decrease in the production constraint. The Lagrange multiplier is approximately equal to the change in P(x, y) given a one unit increase in the budget constraint. The Lagrange multiplier is approximately equal to the change in P(x, y) given a five unit decrease in the budget constraint. 21.-/0.43 pointsHHCalc6 15.3.030. Design a closed cylindrical container which holds 84 cm3 and has the minimal possible surface area. What should its dimensions be? r = h = 22.-/0.43 pointsHHCalc6 15.3.032. An international organization must decide how to spend the $4000 they have been allotted for famine relief in a remote area. They expect to divide the money between buying rice at $5/sack and beans at $10/sack. The number, P, of people who would be fed if they buy x sacks of rice and y sacks of beans is given by P = x + 2y + x2y2 . 2 108 What is the maximum number of people that can be fed? people How should the organization allocate its money? The organization should buy sacks of rice and sacks of beans. 23.-/0.54 pointsHHCalc6 15.3.042. Find the minimum distance from the point (1, 2, 8) to the paraboloid given by the equation z = x2 + y2. (Round your answer to four decimal places.)