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.)

Which of the following housing decisions provides a person with both housing and an investment? a. selling a share in a cooperative. b. buying a single-family home. c. renting an apartment. d. subletting a condominium. 2b2t

Jurvin enterprises is a manufacturing company that had no beginning inventories. a subset of the transactions that it recorded during a recent month is shown below. $76,700 in raw materials were purchased for cash. $71,400 in raw materials were used in production. of this amount, $66,300 was for direct materials and the remainder was for indirect materials. total labor wages of $151,700 were incurred and paid. of this amount, $134,300 was for direct labor and the remainder was for indirect labor. additional manufacturing overhead costs of $126,300 were incurred and paid. manufacturing overhead of $126,800 was applied to production using the company's predetermined overhead rate. all of the jobs in process at the end of the month were completed. all of the completed jobs were shipped to customers. any underapplied or overapplied overhead for the period was closed to cost of goods sold.required: 1. post the above transactions to t-accounts.2. determine the cost of goods sold for the period.

Consider how health insurance affects the quantity of health care services performed. suppose that the typical medical procedure has a cost of $160, yet a person with health insurance pays only $40 out of pocket. her insurance company pays the remaining $120. (the insurance company recoups the $120 through premiums, but the premium a person pays does not depend on how many procedures that person chooses to undergo.) consider the following demand curve in the market for medical care. use the black point (plus symbol) to indicate the quantity of procedures demanded if each procedure has a price of $160. then use the grey point (star symbol) to indicate the quantity of procedures demanded if each procedure has a price of $40. q d at p=$160 q d at p=$40 0 10 20 30 40 50 60 70 80 90 100 200 180 160 140 120 100 80 60 40 20 0 price of medical procedures quantity of medical procedures demand if the cost of each procedure to society is truly $160, the quantity that maximizes total surplus is procedures. economists often blame the health insurance system for excessive use of medical care. given your analysis, the use of care might be viewed as excessive because consumers get procedures whose value is than the cost of producing them.