Marginal Analysis:. Doug Ross is a regional sales representative for Specialty B
ID: 1186510 • Letter: M
Question
Marginal Analysis:. Doug Ross is a regional sales representative for Specialty Books, Inc., and sells
textbooks to universities in Midwestern states. Ross' goal is to maximize total monthly commission
income, which is figured at 10% of gross sales. In reviewing monthly experience over the past year, Ross
found the following relations between days spent in each state and monthly sales generated:
If administrative duties limit Ross to only 15 selling days per month, how should he spend them?
I know that the answer will be somehow related to the amount of marginal sales per day, but dont know how exactly to determine the allocation.
Thanks
Explanation / Answer
Days
Kansas Gross Sales
Oklahoma Gross Sales
Nebraska Gross Sales
Kansas Marginal Sales
Oklahoma Marginal Sales
Nebraska Marginal Sales
0
2000
500
1000
0
0
0
1
4000
1500
3500
2000
1000
2500
2
5600
2300
5500
1600
800
2000
3
6800
2900
7000
1200
600
1500
4
7900
3300
8100
1100
400
1100
5
8500
3500
8900
600
200
800
6
8800
3600
9400
300
100
500
7
8900
3600
9600
100
0
200
Since he has only 15 selling days per month, he should spend each day selling at that place where his marginal sales is highest.
For the 1st day, marginal sale at Nebraska is highest (=2500). Hence he should allocate his first day to Nebraska.
For the 2nd and 3rd day, marginal sale at Kansas and Nebraska is highest (=2000). Hence he should allocate his second day to Kansas and Nebraska.
Similarly he should allocate his 4th day to Kansas (=1600) , 5th to Nebraska (=1500), 6th to Kansas (=1200), 7th and 8th to Kansas and Nebraska (=1100 each),9th to Oklahoma (marginal sales=1000), 10th and 11th to Nebraska and Oklahoma (=800), 12th and 13th to Kansas and Oklahoma (=600 each), 14th to Nebraska (=500), 15th to Oklahoma (=400).
Hence he should spend 6 days in Nebraska, 5 days in Kansas and 4 days in Oklahoma.
Days
Kansas Gross Sales
Oklahoma Gross Sales
Nebraska Gross Sales
Kansas Marginal Sales
Oklahoma Marginal Sales
Nebraska Marginal Sales
0
2000
500
1000
0
0
0
1
4000
1500
3500
2000
1000
2500
2
5600
2300
5500
1600
800
2000
3
6800
2900
7000
1200
600
1500
4
7900
3300
8100
1100
400
1100
5
8500
3500
8900
600
200
800
6
8800
3600
9400
300
100
500
7
8900
3600
9600
100
0
200