9781118041581

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)

c05Production.qxd 9/5/11 5:49 PM Page 216