The answer is a resounding no! Management’s objective is to assign its sales force to
maximize total profit. This is just a fixed-input/multiple-product decision. Thus, the com-
pany should assign salespersons to the category of account that generates the greater
marginal profit per unit input. For convenience, Figure 5.5 lists marginal profits (in paren-
theses) for each type of account and for the different sizes of sales force. The profit func-
tion for large accounts indicates that a two-person sales force raises profit from $200,000
to $500,000, implying a marginal profit of $150,000 per person (presumably this minimal
sales force is essential for retaining the firm’s most loyal current clients); going from two
to five salespeople increases profit by $100,000 per individual; and so on.
The optimal allocation is eight salespeople to large accounts and ten to new
accounts. We assign salespersons to accounts in order of marginal profits; that is, the
highest marginal profit assignments are made first. The “first” five individuals serve
large accounts. (Marginal profit is $150,000 and then $100,000 per person.) The “next”
eight individuals serve new accounts. (Marginal profit is $80,000 and then $70,000 per
216 Chapter 5 Production
FIGURE 5.5
Profit Functions for an
Office Supply Firm
The optimal division
of salespeople is 8
individuals to “large”
accounts and 10 to
“new” accounts.
Operating Profit (Thousands of Dollars)
1,400
1,300
1,200
1,100
1,000
900
800
700
600
500
400
300
200
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Number of Salespersons
Large accounts
New accounts
400
610
690
Optimal
allocations
500
800
950
1,040
1,100
930
(150)
(100)
(50)
(70)
(80)
(40)
(30)
(20)
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