A candidate for mayor in a small town has allocated $40,000 for last-minute advertising in the days preceding the electi

[answerhappygod]

A candidate for mayor in a small town has allocated $40,000 for
last-minute advertising in the days preceding the election. Two
types of ads will be used: radio and television. Each radio ad
costs $200 and reaches an estimated 3,000 people. Each television
ad costs $500 and reaches an estimated 7,000 people. In planning
the advertising campaign, the campaign manager would like to reach
as many people as possible, but she has stipulated that at least 10
ads of each type must be used. Also, the number of radio ads must
be at least as great as the number of television ads. How many ads
of each type should be used in order to reach as many people as
possible?
a) (4 pts) Is this a maximization or a minimization problem?
What is the objective?
b) (5 pts) Formulate this problem mathematically. Use R and T to
represent the number of radio and television ads, respectively.
Write down or type the objective function and all constraints
clearly. (Don’t forget the nonnegativity constraints when
applicable.)
c) (8 pts) Set up this problem in Excel and use Solver to find
the optimal value of R and T, i.e., the numbers of radio and TV ads
that maximize the number of people reached.
d) (2 pts) Use Solver to generate a sensitivity report for this
optimization problem. Please label the Excel worksheet containing
the sensitivity report by “Q1_Sensitivity Report”.
e) (4 pts) The candidate for mayor recently raised an additional
$1,000 that can be used to purchase more ads. Based on the
sensitivity report, how many more people can be reached? (Hint: use
the shadow price of the total budget.)