Show that the symmetric rank-one update (2.18) and the BFGS update (2.19) are scale-invariant if the initial Hessian approximations B0 are chosen appropriately. That is, using the notation of the previous exercise, show that if these methods are applied to f (x) starting from x0 Sz0 + s with initial Hessian B0, and to f˜(z) starting from z0 with initial Hessian ST B0S, then all iterates are related by xk Szk + s. (Assume for simplicity that the methods take unit step lengths.)

Acompany has two products: standard and deluxe. the company expects to produce 36,375 standard units and 62,240 deluxe units. it uses activity-based costing and has prepared the following analysis showing budgeted cost and cost driver activity for each of its three activity cost pools. budgeted activity of cost driver activity cost pool budgeted cost standard deluxe activity 1 $ 93,000 2,500 5,250 activity 2 $ 92,000 4,500 5,500 activity 3 $ 87,000 3,000 2,800 what is the overhead cost per unit for the standard units? what is the overhead cost per unit for the deluxe units? (round activity rate and cost per unit answers to 2 decimal places.)activity expected costs expected activity driver activity rate1 93,000 2 92,000 3 87,000 standard activity activity driver activity rate allocated costs1 2 3