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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 ($)
0
$ 10,000
$ 0
$ 6,250
1
25,000
8,750
12,500
2
37,500
16,250
17,500
3
47,500
22,500
21,250
4
55,000
26,250
23,750
5
60,000
28,750
6
62,500
30,000
7
31,250
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.
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