A material is required for a cheap column with a solid circular cross-section that must support a load F* without buckling. It is to have a height L . Write down an equation for the material cost of the column in terms of its dimensions, the price per kg of the material, Cm , and the material density (rho) .The cross-section area A is a free variable: eliminate it by using the constraint that the buckling load must not be less than F crit (equation 5.9). Hence read off the index for ?nding the cheapest tie. Plot the index on a copy of the appropriate chart and identify three possible candidates