SCENARIO: A regional sales rep who calls on dental labs in three states has found the following relations

exist between days spent in each state and monthly sales generated, she has asked you to help

her maximize her monthly commission income which is 10% of gross sales.

Maine

Total

N.H

Total

Vermont

Total

Day

Maine

NH

VT

Days

Sales

Days

Sales

Days

sales

Marginal

Marginal

Marginal

0

$2'000

0

$1'500

0

$1'000

Sales

Sales

Sales

1

5'000

1

3'500

1

2'600

1

$3'000

2

7'500

2

5'300

2

3'700

2

3

9'500

3

6'900

3

4'300

3

4

11'000

4

8'300

4

4'600

4

5

12'000

5

9'500

5

4'800

5

6

12'500

6

10'500

6

4'900

6

7

12'500

7

11'000

7

5'000

7

INSTRUCTIONS:

A. Construct a table showing her marginal sales per day in each state. For example, her first day spent in Maine her sales are $5k, less $2k if she spends no time in Maine. Thus her marginal sales for the first day in Maine are $3k.

B. If the rep can only spend 10 days per month selling , how should she spend them? (Start with highest marginal sales per day and continue on to the next, etc. until she has spent 10 days)

Days in Maine

Days in NH

Days in VT

C. Calculate the reps maximum monthly commission income.

Income

Total Sales

Commission %

$ -

10.00%