Federico and Giulia are two students who majored in foreign languages and who have recently been hired by a company that translates documents. Each of them can spend their days translating documents from English to Italian or Spanish. If Federico spends all his day translating documents to Italian with no Spanish, he can translate 10 documents, and if he spends all his day translating documents to Spanish with no Italian, he can translate 8 documents. If Giulia spends all her day translating documents to Italian with no Spanish, she can translate 8 documents, and if she spends all her day translating documents to Spanish with no Italian, she can translate 20 documents. (a) The company requires its workers to translate 4 documents to Italian and 6 documents to Spanish in a day. Is this feasible for Federico? How about Giulia? (b) Federico and Julia agree to trade documents. Who should specialize in translating documents to Italian if they trade? And who should specialize in translating documents to Spanish if they trade? (c) What is the lowest price of translating a document to Italian (in terms of documents translated to Spanish) that will allow trade to occur? What is the highest price? (Hint: the seller of Italian translations wants high prices and the buyer wants low prices, and both must agree in order for trade to occur.)
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