A Hollywood movie studio is looking for actors, actresses, and singers for a now
ID: 449931 • Letter: A
Question
A Hollywood movie studio is looking for actors, actresses, and singers for a now movie. The position to be filled are one male and one female leading roles, one male two female support roles, and one female singer role. A list of prospective artists, together with their possible roles, is given below, The List includes the salary demanded by each artist (in millions of dollars) along with a projected value added score which is a number from 1 to 10 evaluating the artist’s projected value to the movie.
( Prospective artist) (Specialty) (Binary variable) (Salary in millions) (Projected added value)
Bratt, Benjamin actor (support) Ybb 3 4
Clooney, George actor (lead) Xcg 12 8
Cosby, Bill actor (support) Ycb 4 4
Crowe, Russell actor (lead) Xcr 7 7
Crowe, Russell actor (support) Ycr 7 5
Freeman, Morgan actor (lead) Xfm 5 7
Freeman, Morgan actor (support) Yfm 5 4
Nicholson, Jack actor (support) Ynj 3 4
Nolte, Nick actor (support) Ynn 3 5
Pitt, Brad actor (lead) Xpb 15 10
Washington, Denzel actor (lead) Xwd 10 9
Dukakis, Olympia Actress (support) Ydo 1 3
Jolie, Angeline Actress (lead) Xja 7 8
Jolie, Angeline Actress (Support) Yja 7 8
Lopez, Jennifer Actress (lead) Xlj 10 10
Lopez, Jennifer Singer Zlj 5 4
Madonna Actress (support) Ym 6 5
Madonna Singer Zm 4 5
Midler, Bette Actress (support) Ymb 3 5
Midler, Bette Singer Zmb 3 6
Boberts, Julia Actress ( support) Yrj 7 8
Also given are the binary decision variables indicating whether an artist is hired or not in a role. The X-variables are for lead actors or actresses, the Y-variables are for support actors or actresses, and the Z variables are for singers. For example, XCR=1 if Russell Crowe is hired as a lead actor, and XCR=0 if he is not. Similarly, YCR=1 if Russell Crowe is hired as a support actor, and YCR=0 if he is not.
The studio has a budget of $30 million. They want to select a subset of these artists to maximize the movie’s projected value without going over budget. They assume that the movie’s projected value equals the sum of the value of each participant. When choosing cast members, the producers must take a number of conditions into consideration, which are given below. You are going to build, in several steps, the algebraic integer linear model for choosing artists for this movie in such a way that the value added is as large as possible, without going over the budget.
Answer each question in algebraic format using only the binary decision variables provided in the table above. Some of the question involving constraints may require more then on constraints. Be sure to write all constraints under the appropriate headings.
a) Write the objective function and indicate whether we have a minimization or maximization problem. You may omit repetitive terms, as long as you specify at least 5 terms, and the pattern is clear
b) Write the constraint requiring that the total cost should not exceed $30 million. You may omit repetitive terms as long as you specify at least 5 terms, and the pattern is clear.
c) An actor cannot be chosen for both the lead and support male roles. Also an actress cannot be chosen for both the lead and support female roles. However, an actress who can sing could be chosen to both act and sing if necessary.
d) Exactly one actor must be chosen for the lead male role and one actress for the lead female role. Also exactly one actor is chosen for the support male role and exactly to actresses for the support female role. Finally exactly one singer must be chosen. (So you need 5 separate constraints here.)
e) Actor Benjamin Bratt and actress Julia Roberts used to date other and then they broke up. So to avoid awkwardness both of them together should not be hires.
f) Actor Brad Pitt and actress Angelino Jolie are married. They have made it clear to producers that either both or neither one should be hired.
g) The directors have started that if Morgan Freeman is the lead actor and Jack Nicholson is the support actor, then Jennifer Lopez should not be the lead actress.
Explanation / Answer
a)The objective Function is to minimixe the Cost=
Minimize
z=$30 million
_____________________________________________________________________________
b)Subject to the constraints
X1cg +X2ja<19
Y1bb+Y2do+Y3mb<7
Z1m<4
X1cg ,X2ja,Y1bb,Y2do,Y3mb,Z1m >0
_________________________________________________________________________________
c)Subject to the constraints
X1cg +X2ja<19
Y1bb+Y2do+Y3mb<7
Zmb<3
X1cg ,X2ja,Y1bb,Y2do,Y3mb,Z1mb >0
--------------------------------------------------------------------------------------------
g)Subject to the constraints
X1fm+X2ja<12
Y1nj +Y2m+Y3do<10
Z1mb<3
X1fm,X2ja,Y1nj ,Y2m,Y3do,Z1mb>0
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.