1. [-/6 Points] DETAILS MY NOTES Four hundred eighty dollars are available to fence in a rectangular garden. The fencing for the north and south sides of the garden costs $5 per foot and the fencing for the east and west sides costs $15 per foot. Find the dimensions of the largest possible garden. (Give exact answers.) ft (north side) Ift (east side) ft (south side) ft (west side) Submit Answer 2. [-/6 Points] DETAILS MY NOTES The amount of space required by a particular firm is given below, where x and y are, respectively, the number of units of labor and capital utilized. f(x, y) = 1000 6x2 + yz Suppose that labor costs $480 per unit and capital costs $40 per unit and that the firm has $4000 to spend. Determine the amounts of labor and capital that should be utilized in order to minimize the amount of space required. Hint: To minimize f(x, y) it is enough to minimize the expression 6x2 + y2. (Give exact answers.) units of labor units of capital Submit Answer 3. [-/6 Points] DETAILS MY NOTES A monopolist manufactures and sells two competing products, call them I and II, that cost $34 and $28 per unit, respectively, to produce. The revenue from marketing x units of product I and y units of product II is R(x, y) = 102x + 120y - 0.04xy - 0.1x2 - 0.2y2. Find the exact values of x and y that maximize the monopolist's profits. y = Submit Answer 4. [-/9 Points] DETAILS MY NOTES Find the values of x, y, and z that minimize xy + 4xz + 4yz subject to the constraint 16 - xyz = 0. (Give exact answers.) X =| Z = Submit Answer 5. [-/9 Points] DETAILS MY NOTES Use Lagrange multipliers to find the three positive numbers whose sum is 12 and whose product is as large as possible. (Give exact answers.) (smallest value) (largest value) Submit Answer 6. [-/9 Points] DETAILS MY NOTES A shelter for use at the beach has a back, two sides, and a top made of canvas. Find the dimensions that maximize the volume and require 96 square feet of canvas. (Give exact answers.) Ift Submit