The design of a stepped drive shaft to drive centrifugal pum

The design of a stepped drive shaft to drive centrifugal pump with pulley B and pulley C by considering the critical whirling frequencies in Figure Q3. Steps:  Determine suitable diameter D1 and D2 for the two shaft lengths L1*and L2* for each pulley to absorb 113 Nm. The shaft is made of steel and let the safety factor be SF = 2 for yield by the maximum shear-stress criterion.  The motor is capable to deliver power P = 6000 kW, determine the maximum frequency range f that can be operated.  Suggest a possible design to hold the shaft with bearings to avoid whirling occurrence. Justify you design of choosing how many and what type of bearing (short or long bearings) to be used. You must choose the available products from the product catalogues and also try to minimise the cost.