END

Part III Principles in Practice

OBJECTIVE FUNCTION VALUE

$2427\mathrm{.}66700$

NO$.$ ITERATIONS $=5$

RANGES IN WHICH THE BASIS IS UNCHANGED:$($f$)$ Reconsider the All$-$Balsa problem formulation and suppose that instead of having

$400$ bf of raw material available at $$1\mathrm{.}50/$bf$,$ All$-$Balsa faces a two$-$tier pricing scheme

such that the first $200$ bf$/$week costs $$2\mathrm{.}00/$bf$,$ but any amount above $200$ bf$/$week up to a

Chapter $16$ Aggregate and Workforce Planning $601$

limit of an additional $300$ bf$/$week costs $p$/$bf$.($Note: p is a constant, not a variable, and

we cannot purchase the $p$/$bf raw material unless we first purchase $200$ bf of the

$$2\mathrm{.}00$ raw material.$)$ To modify the LP to compute an $$optimal$$ production$/$advertising

policy, we define

RM$1=$ bf of raw material purchased at $$2\mathrm{.}00/$bf

RM$2=$ bf of raw material purchased at $p$/$bf

To formulate an appropriate LP to represent this new pricing scheme, we first replace

$1\mathrm{.}5$RM in the objective function by $2$RM$1+$ pRM$2.$

i$.$ If p $>2,$ what other changes in the previous LP make it properly reflect the new

pricing scheme?

ii$.$ If p what other changes in the previous LP make it properly reflect the new

pricing scheme