Given the total slaes, compute the marginal sales, also compute the maximum monthly commission income.
Meredith Grey is a regional sales representative for Dental Laboratories, Inc., a company that sells alloys created from gold, silver, platinum, and other precious metals to several dental laboratories in Washington, Oregon, and Idaho. Grey's goal is to maximize total monthly commission income, which is figured ay 8 percent of gross sales. In reviewing monthly experience over the past year, Grey found the following relations between days spent in each state and monthly sales generated:
Washington
|
Oregon
|
Idaho
|
Days
|
Gross sales ($)
|
Days
|
Gross sales ($)
|
Days
|
Gross sales ($)
|
0
|
$ 10,000
|
0
|
$ 0
|
0
|
$ 6,250
|
1
|
25,000
|
1
|
8,750
|
1
|
12,500
|
2
|
37,500
|
2
|
16,250
|
2
|
17,500
|
3
|
47,500
|
3
|
22,500
|
3
|
21,250
|
4
|
55,000
|
4
|
26,250
|
4
|
23,750
|
5
|
60,000
|
5
|
28,750
|
5
|
25,000
|
6
|
62,500
|
6
|
30,000
|
6
|
25,000
|
7
|
62,500
|
7
|
31,250
|
7
|
25,000
|
a. Construct a table shoeing Grey's marginal sales per day in each state.
b. If administrative duties limit Grey to only 10 selling days per month, how should they be spent to maximize commission income?
c. Calculate Grey's maximum monthly commission income.