#3
15
points
The Profit & Gamble Co. produces cleaning products for home use. This is a highly competitive market, and the company continually struggles to increase its market share. Management has decided to undertake a major new advertising campaign that will focus on the following three key products:
·
a
spray prewash stain remover
·
a
new liquid laundry detergent
·
a
well-established powder laundry detergent
This
campaign will use both television and print media. A commercial has been developed to run on national
television
that will feature the liquid detergent to help establish this new
product. The advertisement for the print media
will
promote all three products and will include cents-off coupons that
consumers
can use to purchase the products at reduced prices. Management has set minimum goals for the advertising
campaign:
1) the
stain
remover should capture an additional 3% of its
market
2) the
new
liquid detergent should gain 18% of the laundry detergent
market
3) a 4%
increase of this same market should be captured by the powder
detergent
The
following table shows the estimated increase in these market shares for
each unit of advertising in the
respective
outlets. (A unit is a standard block of advertising that Profit &
Gamble
commonly purchases, but other amounts also are allowed.) The reason for the –1% for the powder
detergent in the Television column is that the TV commercial featuring the
new
liquid detergent will take away sales from the powder detergent. The bottom row of the table shows the
cost
per unit of advertising for each of the two outlets.
Increase in Market Share per Unit of Advertising |
|||
|
|||
Product |
Television |
Print Media |
MinimumRequired Increase |
Stain
remover |
0% |
1% |
3% |
Liquid
detergent |
3% |
2% |
18% |
Powder
detergent |
-1% |
4% |
4% |
Unit cost |
$1
million |
$2
million |
|
Management’s
objective is to determine how much to advertise in each medium to meet the
market share goals at minimum total cost.
Define
the problem.
Build
one or more model(s).
Solve the model.
In this case, you will use a graphical method to solve it. (In addition, you will use a computer software method (STORM) in class on Thursday.)
Submit the following,
stapled in order:
a) cover page (see handout #1 for a list
of the
items that must be on the cover page)
b) the problem definition
c) the linear programming
model
d) the graphical solution: the potential optimal solutions should
be
clearly marked and the calculations for the final solution
shown
e) the analysis: memo to management to explain your
findings
Note: As with all assignments, this one must be presented in a
professional manner, typed, spell-checked, and grammar-checked. See handout #1 for more
information.