Answer Happy

It is desired to build a warehouse of width x₁, height x2, and length x3 (in metres), with capacity 1500 m³. Building costs per square metre are: walls £4, roof £6, floor plus land £12. For aesthetic reasons, the width should be twice the height. State the problem which determines the dimensions of the ware- house of minimum cost and write down the KT conditions. By eliminating x₁ and x3, show that to the nearest metre, x₂ = 10 minimizes the cost, and hence find x, and x3. Determine the optimum multipliers in the KT conditions. It can be shown that changing c;(x) = 0 to ci(x) = e, in the problem induces a change A;e; (to first order) in f(x) at the resulting solution. Estimate the change in cost on reducing the required capacity by 10 per cent. Practical Optimization by R. Kazemi Matin (rkmatin [email protected]) QUI