Other Production Decisions 21510 to 30 percent lighter) in myriad parts throughout vehicle bodies, manufac-
turers are hoping to trim as much as 500 or 700 pounds per vehicle and, con-
sequently, raise fuel efficiency by 5 to 10 MPG. By 2016, Corporate Average
Fuel economy (CAFE) standards will require carmakers’ vehicles and trucks
to achieve an average of 35.6 MPG.^12
Like the multiplant and multiproduct problems already discussed, car-
makers face an important constraint. However, here the constraint relates to
average fuel efficiency (rather than limited inputs). To meet tougher CAFE
standards, carmakers have several options. (1) they can lighten the weight of
various model cars and trucks by substituting aluminum for steel, and (2) they
can tilt their production mix of vehicles toward lightweight compact cars and
away from heavier trucks. However, both options are expensive. Even after a
recent narrowing of the price gap, aluminum is still about 30 percent more
expensive than steel in vehicles. In many instances, assembly-line processes
must be modified to accommodate aluminum. In turn, carmakers earn signif-
icantly higher margins and profit on heavier vehicles—full-size luxury sedans,
roomy minivans and SUVs, and trucks.
Thus, in seeking maximum profit subject to meeting stricter CAFE stan-
dards, carmakers face a number of complicated trade-offs. To what degree is it
best for aluminum to replace steel in various models? In addition, how should
carmakers fine-tune their mix of vehicles to maximize their overall profit? In
all this, there is one piece of good news. Aluminum producers are jumping at
the chance to overturn steel’s seven-to-one usage advantage in favor of a some-
thing closer to a 50–50 split. In fiercely fighting for the auto business, alu-
minum and steel producers have already begun offering significant price
reductions to auto makers.(^12) This account is based in part on R. G. Mathews, “Aluminum Tests Its Mettle against Steel in Drive
for Lighter Cars,” The Wall Street Journal, March 16, 2011, p. B1.
Allocating a Sales Force
Revisited
Recall that the key issue for the office supply firm was how to divide its 18-person sales
force between large accounts (firms already under contract with the company or a com-
petitor) and new accounts (firms without a current rental contract). To address this
problem, five senior sales managers have put to paper their best estimate of the profit
functions for both types of accounts; these functions are shown in Figure 5.5. There is
general agreement that the large accounts are more profitable than the new accounts.
In Figure 5.5, the profit function for large accounts is uniformly greater than that for new
accounts. (For instance, assigning five salespeople to the former generates $800,000,
whereas assigning the same number to new accounts generates only $400,000.) In light
of the profit curves, would senior sales managers be justified in allocating all 18 sales-
people to large accounts?
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