6 A pipe is to be built from pointA

Question 6 0 / 5 pt A pipe is to be built from point A to point D and must pass through regions where construction costs differ. The unit cost (in dollars per kilometre) from B to C' is 5 times as much as the unit cost from A to B and the unit cost from C to D is 3 times as much as the cost from A to B. A B 4km C 2km D - x- - y . Z 20km For simplicity, let the unit cost from A to B be $1/km. You are required to use the method of Lagrange multipliers to find , y and z such that the total construction cost will be minimized. A formulation to the problem is: Maximize f(I, y, z) = 1+3\\y- +4+5V23+16 O subject to the constraint g(x, y, z) = = + y + 2 - 20 =0 Maximize f(x, y, 2) = =+5\\y +4+32+16 O subject to the constraint g(x, y, z) = = + y + z - 20 =0 Maximize f(I, y, 2) = x +3 y2 + 16 +5\\22+4 O subject to the constraint g(x, y, z) = = + y + z - 20 =0 Maximize f(I, y, 2) = x +5Vy2 +16 +3V22+4 O subject to the constraint g(x, y, 2) = = + y + 2 - 20 =0