POSNER, Chief Judge.

Modern Dairy of Champaign, Inc. went into bankruptcy and the trustee brought adversary actions to recover payment for deliveries of milk that the dairy had made to two school districts, McLean and Champaign. The districts conceded nonpayment but sought to offset, against the payments due, damages that they claimed to have sustained when the dairy had stopped delivering milk to them. They argued that their contracts with the dairy were requirements contracts, by which they mean not only that they agreed to buy all their requirements of milk from the dairy, which is the usual meaning of the term, e.g., Canteen Corp. v. Former Foods, Inc., 238 Ill.App.3d 167, 179 Ill.Dec. 342 606 N.E.2d 174, 183 (1992); Zayre Corp. v. S.M. R. Co., 882 F.2d 1145, 1154-55 (7th Cir. 1989) (applying Illinois law); Orchard Group, Inc. v. Konica Medical Corp., 135 F.3d 421, 429-30 (6th Cir. 1998); Mid-South Packers, Inc. v. Shoney's, Inc., 761 F.2d 1117, 1120-21 (5th Cir. 1985) (per curiam), but also that, in exchange for this commitment, the dairy agreed to supply all those requirements. The bankruptcy judge agreed with the school districts and granted summary judgment for them, and the district judges affirmed. The trustee appeals, arguing that these were not requirements contracts and therefore that the dairy was under no obligation to continue supplying milk to the districts. If this is right, there was no breach of contract by the dairy, and the school districts are not entitled to claim damages as an offset to their own breach. The issue is governed by the common law of Illinois.

The contracts do not expressly obligate the dairy to supply the districts with their requirements for milk. But such an obligation can be implicit as well as express, Essco Geometric v. Harvard Industries, 46 F.3d 718, 728-29 (8th Cir. 1995); O.N. Jonas Co. v. Badische Corp., 706 F.2d 1161, 1164-65 (11th Cir. 1983) (per curiam); R.L. Kimsey Cotton Co. v. Ferguson, 233 Ga. 962, 214 S.E.2d 360, 362-63 (Ga. 1975), and the inference would be compelling if the contracts forbade the districts to turn elsewhere for milk. A buyer would be unlikely to commit to take all his requirements for some good from the seller if the seller had no reciprocal obligation to supply those requirements. That would put the buyer at the seller's mercy. Contract law, in inferring an obligation to sell in these circumstances, would be performing its frequent office of interpolating a contractual term to which the parties would almost certainly have agreed expressly had they thought about the matter. E.g., In re Wallis, 276 Ill. App.3d 1053, 213 Ill.Dec. 507, 659 N.E.2d 423, 427 (1995); Market Street Associates Limited Partnership v. Frey, 941 F.2d 588, 596 (7th Cir. 1991). The term sought to be interpolated here closely resembles the best-efforts obligation that is read into exclusive-dealing contracts (see, e.g., Wood v. Duff-Gordon, 222 N.Y. 88, 118 N.E. 214 (1917) (Cardozo, J.); Advent Systems Ltd. v. Unisys Corp., 925 F.2d 670, 679-80 (3d Cir. 1991); E. Allan Farnsworth, Contracts § 7.17, pp. 509-11 (3d ed. 1999)) for the same reason: the dealer could "hold up" his supplier if the latter could not terminate the contract even though the dealer was making no effort to sell the supplier's products.

So we must consider whether the school districts obligated themselves to buy their milk requirements from the dairy, for if so that triggered the reciprocal obligation to supply those requirements, and then the dairy's termination of deliveries was a breach of contract entitling the districts to an offset. The districts had invited bids, and the bid specifications provided that the milk would be supplied in quantities to be determined by the district's food manager. The specifications contained an estimate of the quantities likely to be demanded. The dairy submitted bids, listing the price of its milk, and the districts accepted the bids and issued purchase orders. McLean's order is for "milk products for the 1996/97 year as per your bid," and Champaign's is for milk "to be ordered throughout the 1996-97 school year . . . as per . . . your bid quotation." The dairy ceased deliveries in October 1996, well short of the end of the school year (indeed quite near the beginning).

Nothing in the scanty documents that record the parties' deal explicitly requires the school districts to take all, or indeed any, of their milk needs from the dairy. If in the course of the school year another dairy offered to supply the districts' needs at a lower price, Modern Dairy could not point to any contractual language indicating that it would be a breach of contract for the districts to switch. So far as the contractual documents are concerned, all there is is the dairy's agreement to sell milk to the districts at a specified price that it cannot raise during the school year: in other words, a buyer's option. A clause requires the dairy to pick up any unused milk the day before scheduled vacation days and credit the school districts; and it would be odd, to say the least, if the dairy had agreed to do this with respect to milk supplied by other dairies; and so it could be argued that the clause assumes that the school districts were obligated to take all their requirements from Modern Dairy. But while this could be argued, it is not. The parties treat the clause as requiring Modern Dairy merely to pick up any unused milk that it had sold the districts.

The parties introduced extrinsic evidence to show that the districts were, or were not, obligated to buy all their requirements from Modern Dairy. The evidence turns out to be irrelevant. The districts put in evidence that Modern Dairy was indeed the low bidder, that the dairy was willing to supply all the milk that the districts wanted during the school year, that it did supply milk in the quantities ordered — until October — and that when it stopped supplying milk the districts turned to other dairies that charged higher prices (otherwise, the districts would have sustained no damages from the alleged breach). This evidence is consistent with the hypothesis of a buyer's option. The dairy put in equally unhelpful evidence that the contract did not obligate it to supply the districts' requirements, which was just a legal conclusion.

When a contract is ambiguous, extrinsic evidence is admissible to disambiguate it; and the determination of the contract's meaning becomes a matter for trial. E.g., Farm Credit Bank v. Whitlock, 144 Ill.2d 440, 163 Ill.Dec. 510, N.E.2d 664, 667 Craigs, Inc. v. General Electric Capital Corp., 12 F.3d 686, 691 (7th Cir. 1993); Exxon Corp. v. Crosby-Mississippi Resources, Ltd., 154 F.3d 202, 207 (5th Cir. 1998). This is true even if there are no credibility issues, that is, even if each piece of evidence is accepted as authentic and true, and the only issue is the proper inference from the evidence considered as a whole. Mathews v. Sears Pension Plan, 144 F.3d 461, 468 (7th Cir. 1998). In this case, however, the extrinsic evidence sheds no light on the contract's meaning, and so there is nothing for a trial. McElroy v. B.F. Goodrich Co., 73 F.3d 722, 727 (7th Cir. 1996). It is just like a case in which the contract is ambiguous but there is no extrinsic evidence available to disambiguate it.

Even in such a case, however, if the contract is not a single document, but must be reconstructed from a series of documents, the determination of the contract's meaning is an issue for trial. Glass v. Kemper Corp., 133 F.3d 999, 1001 (7th Cir. 1998); Western Industries, Inc. v. Newcor Canada Ltd., 739 F.2d 1198, 1205 (7th Cir. 1984); Meyers v. Selznick Co., 373 F.2d 218, 223 (2d Cir. 1966) (Friendly, J.). And this is such a case, because the contract between the dairy and the school districts does not reside within the borders of a single document but must be reconstructed from several documents — the request for bids, the bids themselves, and the purchase orders. But no purpose would be served by remanding the case for a trial. No reasonable trier of fact could infer from these documents that the school districts committed to buy their entire milk requirements from the dairy, thereby imposing on the latter an obligation to supply those requirements. There is nothing to make such an interpretation more plausible than the alternative hypothesis of a buyer's option. The districts could have presented evidence of the custom of the parties or the industry, e.g., Magallanes Investments, Inc. v. Circuit Systems, Inc., 994 F.2d 1214, 1219 n. 6 (7th Cir. 1993); Remus v. Amoco Oil Co., 794 F.2d 1238, 1242 (7th Cir. 1986); Nanakuli Paving Rock Co. v. Shell Oil Co., 664 F.2d 772, 794 (9th Cir. 1981), showing that the form of words that the parties used, or their course of previous dealings, showed that they intended this to be a requirements contract. They presented no such evidence; nor do they request an opportunity to do so.

Twice, though, we've mentioned the alternative of a buyer's option; and it might seem that the districts should be complaining not of the breach of a requirements contract but of the dairy's refusal to honor the option. There is language, particularly in McLean's request for bids, suggesting that Modern Dairy committed not only to a price, but also to satisfying the school district's school-year milk needs (for example, "The vendor is required to furnish to each location the number of milk containers requested by the Food Service Supervisor or school principal"). However, the school districts insist that the issue is whether they were obligated to buy all their milk requirements for the school year from Modern Dairy, and they assume that if the answer is "no," they lose. They may be right. A seller's firm offer to supply the buyer's needs for some good at a specified price and other terms is enforceable under the Uniform Commercial Code even though the buyer makes no reciprocal commitment to buy all its needs from this seller, but unless the offer is supported by consideration, it is revocable after three months. UCC 2-205, 810 ILCS 5/2-205; Mid-South Packers, Inc. v. Shoney's Inc., 761 F.2d 1117, 1121 (5th Cir. 1985) (per curiam). The common law doesn't have the deadline, but requires consideration. Restatement (Second) of Contracts § 87 (1981); Merritt-Campbell, Inc. v. RxP Products, Inc., 164 F.3d 957, 963-64 (5th Cir. 1999). The school districts do not argue that either condition was satisfied. Their case stands or falls on whether they were obligated to buy all their milk requirements from Modern Dairy. There is no evidence that they were, and so they lose.

The judgments are reversed and the cases remanded for further proceedings consistent with this opinion.

Reversed and Remanded.