John Smith is a regional sales representative for Snappy Tools, Inc., and sells
ID: 1199540 • Letter: J
Question
John Smith is a regional sales representative for Snappy Tools, Inc., and sells hand tools to auto mechanics in New England states. Smith’s goal is to maximize total monthly commission income, which is figured at 10% of gross sales. In reviewing experience over the past year, Smith found the following relations between days spent in each state and weekly sales generated.
1. Construct a table showing Smith’s marginal sales per day in each state.
2. If Smith is limited to 7 selling days per week, how should they be spent?
3. Calculate Smith’s maximum weekly commission income.
Days
Vermont
Sales
New
Hampshire
Sales
Maine
Sales
0
$ 3,000
$ 3,000
$1,900
1
10,000
7,000
5,200
2
15,000
10,600
7,400
3
19,000
13,800
8,600
4
22,000
16,600
9,200
5
24,000
19,000
9,600
6
25,000
21,000
9,800
1. Construct a table showing Smith’s marginal sales per day in each state.
2. If Smith is limited to 7 selling days per week, how should they be spent?
3. Calculate Smith’s maximum weekly commission income.
Explanation / Answer
Q1. Smith is able to generate sales of $10,000 in 1 day in Vermont while in 2 days he is able to generate sale of $15,000.
So, marginal sales of Smith for 2nd day in Vermont can be calculated as follows –
Marginal sales for 2nd day = Total sales in 2 days – Total sale in 1 day
= $15,000 - $10,000
= $5,000
Thus, Smith’s marginal sale for 2nd day in Vermont is $5,000.
Similarly, marginal sales for each day in each respective state can be calculated.
Following table shows that Smith’s marginal sales per day in each state based on above mentioned procedure–
Days
Vermont
Sales
Marginal sales per day in Vermont
New Hampshire
Sales
Marginal sales per day in New Hampshire
Maine sales
Marginal sales per day in Maine
0
$3,000
-
$3,000
-
$1,900
-
1
10,000
$7,000
7,000
$4,000
5,200
$3,300
2
15,000
$5,000
10,600
$3,600
7,400
$2,200
3
19,000
$4,000
13,800
$3,200
8,600
$1,200
4
22,000
$3,000
16,600
$2,800
9,200
$600
5
24,000
$2,000
19,000
$2,400
9,600
$400
6
25,000
$1,000
21,000
$2,000
9,800
$200
Days
Vermont
Sales
Marginal sales per day in Vermont
New Hampshire
Sales
Marginal sales per day in New Hampshire
Maine sales
Marginal sales per day in Maine
0
$3,000
-
$3,000
-
$1,900
-
1
10,000
$7,000
7,000
$4,000
5,200
$3,300
2
15,000
$5,000
10,600
$3,600
7,400
$2,200
3
19,000
$4,000
13,800
$3,200
8,600
$1,200
4
22,000
$3,000
16,600
$2,800
9,200
$600
5
24,000
$2,000
19,000
$2,400
9,600
$400
6
25,000
$1,000
21,000
$2,000
9,800
$200
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