Minimize: Subject to the constraints: 3x₁ + 2x2 + x3 ≥ 23 X1 + X3 ≥ 10 8x1 + x2 + 2x3 ≥ 40 X1 > 0 C = 4x₁ + x2 + x3 x2 > 0 X3 ≥ 0

A cylindrical tank with a closed top is to be constructed to hold a fixed volume of 16, 0007 m³. Find he dimensions of the tank (radius r and height h) with the smallest possible total surface area. ou must justify your answer really does give the minimum surface area. constraint equation in terms of r and h: objective function in terms of r: dimensions of optimal tank (in meters): radius (r) Allqmie height (h)

5 The manager of a garden store wants to build a rectangular enclosure on the store's parking lot with an area of 800 square feet. The cost of the fencing used on each of the widths is $5/foot and the cost of the fencing used on each of the lengths is $10/foot. Find the length and the width of this enclosure, so that the cost needed for the fence is at a minimum. Find that minimum cost also.