Your company adjusts the salary of its CEO by a linear functional x of three qua

Question

Your company adjusts the salary of its CEO by a linear functional x of
three quantities: u = change in stock price, v = change in pro ts, w =
change in number of employees. The current formula is < x; x >= 4u +
2v + 5w, represented by a vector (4; 2; 5) 2 X
New Federal law requires that all such functionals must give 0 when eval-
uated on any vector in the subspace M X generated by (1,1,-2). Your
functional is noncompliant because it does not lie in the annihilator space
M?, and you need to adjust it to a compliant functional m0
. The CEO
insists that you do this in such a way as to minimize the sum d of the
absolute values of the changes in the coecients.
(a) Find d by duality, then nd m0
by alignment.
(b) Solve the problem for the case where M is generated by (1,2,-2). Show
that in this case there are many choices for m0
that all lead to the same
d.
(c) The adjustment y = x ?? m0
can be obtained by restricting x to
M, then doing a Hahn-Banach extension to all of X. In this case the
region where jjxjj 1 is just a cube. Give a geometrical explanation of
why the solution was unique in the rst case but not in the second, and
invent a choice for M that allows even more
exibility in the solution.
(d) Solve parts (a) and (b) with a di erent norm, by choosing m0
to mini-
mize the maximum d of the absolute values of the changes in the coef-
cients. Determine whether or not the solution in part (b) is unique.
8

our company adjusts the salary of its CEO by a lincar functional r of thre quantities: u change in stock price, U-change in profits, w = change in number of employees. The current formula is = 421 + 20 + 5w, represented by a vector (4,2,5) E X* New Fedcral law requires that all such functionals must give 0 when eval- uated on any vector in the subspace M C X generated by (1,1.-2). Your functional is noncompliant because it docs not lie in the annihilator space M1, and you need to adjust it to a compliant functional mo The CEO insists that you do this in such a way as to minimize the sum d of the absolute valucs of the changcs in the cocfficicnts (a) Find d by duality, then find m? by align!nent (b) Solve the problem for the case where M is gencrated by (1,2,-2). Show that in this case there are many choices for m that all lead to the same (c) The adjustment y- mocan be obtaincd by restricting z* to M, then doing a Hahn-Banach extension to all of X. In this case the region where ll?

Explanation / Answer

Answer:

Dear Student Thank you for using Chegg !! Current Salary of Juan = 54000 $ Salary increse 1/5 its value after each year Let the last year salary be x Calculating relation between last year salary and present salary Present Salary = x + (1/5)x Hence from above relations (6/5)x = 54000 $ x = 45000 Hence last year salary is 45000 $ Through same relation salary in previous year = Present salary* 5/6 Salary 2 years before = 45000*5/6 $ = 37500 $ Salary 3 years before = 37500*5/6 $ = 31250 $ Solution

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.