#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
a model.
Solve the model.
In this case, you will use a graphical method to solve it.
Submit the following,
stapled in order:
a) cover page (see
handout #1, page 3 for a list of the items that must be on the cover page)
b) Executive Summary: memo to the client to explain your findings
(see handout #1, page 4 for a list of what this memo must contain)
c) the problem
definition
d) the decision variables and linear programming
model
e) the graphical
solution: the potential optimal
solutions should be clearly marked and the calculations for the final solution
shown
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.