#3

# Mgmt 380

## DUE:Tuesday, February 6

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.

#### Minimum

Required

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.

###### What is the goal?What is the research question or problem statement?What are the decision variables?

Build one or more model(s).

###### In this case, you will build a linear programming model.What is the objective function?What are the constraints?

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.