Choose the correct alternative according to the
text.
Opportunity Cost
This phenomenon goes by the name of ‘opportunity
cost,’ since by not investing in more equipment and
a more rigid production flow, the company is forgoing the opportunity to earn increased profits. These
costs are every bite as real as the payment of dollars
out-of-pocket.
This notion _______ opportunity cost can be reinforced _________ a famous saying ______ Benjamin
Franklin, no slouch himself _________ operations
management. To make the point, however, we must
make a brief excursion into logic. One truth of logic is
the validity of the so-called contrapositive, which says
simply that if the statement “If A, then B” is true, then
it is also true that “If not B, then not A.” That is, of every
time A occurs B follows, then we can be sure that if B
does not occur, then A did not occur as well. Enough
logic then, and back to Ben Franklin.
One of his Poor Richard sayings is that “A penny saved
is a penny earned.” We have all recognized the truth of
that since childhood, but I assert that by this saying
Ben showed us he knows everything about opportunity cost. After all, what is the contrapositive of “A
penny not earned is a penny not saved (i.e., a penny
sent). All we are saying by this notion of opportunity
cost is that “a penny not earned (an opportunity forgone) is a penny spent.” We shall often have occasion
to consider opportunity costs, in analyzing and deciding various operations issues.
SCHMENNER, Roger W. Production/Operations Management. 5th
Edition. Prentice-Hall, 1993.
Opportunity Cost
This phenomenon goes by the name of ‘opportunity cost,’ since by not investing in more equipment and a more rigid production flow, the company is forgoing the opportunity to earn increased profits. These costs are every bite as real as the payment of dollars out-of-pocket.
This notion _______ opportunity cost can be reinforced _________ a famous saying ______ Benjamin Franklin, no slouch himself _________ operations management. To make the point, however, we must make a brief excursion into logic. One truth of logic is the validity of the so-called contrapositive, which says simply that if the statement “If A, then B” is true, then it is also true that “If not B, then not A.” That is, of every time A occurs B follows, then we can be sure that if B does not occur, then A did not occur as well. Enough logic then, and back to Ben Franklin.
One of his Poor Richard sayings is that “A penny saved is a penny earned.” We have all recognized the truth of that since childhood, but I assert that by this saying Ben showed us he knows everything about opportunity cost. After all, what is the contrapositive of “A penny not earned is a penny not saved (i.e., a penny sent). All we are saying by this notion of opportunity cost is that “a penny not earned (an opportunity forgone) is a penny spent.” We shall often have occasion to consider opportunity costs, in analyzing and deciding various operations issues.
SCHMENNER, Roger W. Production/Operations Management. 5th
Edition. Prentice-Hall, 1993.
Gabarito comentado
Alternativa correta: A
1) Tema central: A questão testa compreensão de uma noção lógica fundamental — a contrapositiva — presente no texto que relaciona sentido comum (ditado de Benjamin Franklin) com o conceito econômico de opportunity cost. Saber identificar forma lógica e negar corretamente termos é essencial em questões de interpretação.
2) Resumo teórico: A regra válida em lógica proposicional é: se “Se A, então B” (A → B) é verdadeira, então sua contrapositiva “Se não B, então não A” (¬B → ¬A) também é verdadeira. Não confundir com a conversa (B → A) ou a inversa (¬A → ¬B), que não são logicamente equivalentes. Fonte: Copi, Introduction to Logic; também ilustrado no trecho de Schmenner (texto-base).
3) Justificativa da alternativa A: A reproduz exatamente a afirmação do texto: “If A, then B” é verdadeira ⇒ “If not B, then not A” também é verdadeira. Isso é a contrapositiva e corresponde à regra lógica citada pelo autor. Portanto, A é correta.
4) Análise das incorretas:
B — Inverte a verdade inicial: diz “If A, then B” é não verdadeira; mesmo assim afirma a contrapositiva. Troca o status de verdade e está incorreta.
C — Afirma “If B, then A” e nega a contraposição; confunde com a conversa, que não é equivalente; afirmação falsa.
D — Forma confusa e invertida: “A seldom occurs B follows” (frase gramaticalmente e logicamente equivocada) e conclui sobre ocorrência de B ⇒ A não ocorreu — contrária à contrapositiva.
E — Afirma que “Every time A occurs B follows, then we can assure that if B occurs, then A did not occur as well.” Contraditória: a consequência correta seria, no máximo, garantir a contrapositiva (se B não ocorre, A não ocorreu). Aqui faz o oposto, portanto errada.
5) Estratégia prática: Procure identificar a estrutura “If A, then B”, sublinhe negações (not B / not A) e teste exemplos concretos. Se a alternativa troca posições (converse) ou nega o fato inicial, desconfie — converse e inversa são armadilhas frequentes.
Referências rápidas: Schmenner (texto-base); Copi, Introduction to Logic (regra da contrapositiva).
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