When drafting and negotiating the contract with your customer, you need to check all the related clauses careflly to avoid any contradiction; and here is normally a clause called Priority to define in case of contradiction which one shall take priority.
But if contradiction is found only after contract signing, and both parites disputes on the priority of the clauses, the things will be more complicated. If the dispute has to be solved by arbitrition or court, there will be cost, and the result is subject to the applicable law. The best way out is to negotiate with your customer and try best to achieve agreement.
An Order of Precedence clause in the contract will usually describe the hierarchy of the various sections of the contract e.g. the Ts & Cs, the Technical Specification, the works Programme, any other documents incorporated by reference. Conflicting clauses in an umbrella agreement may be stated to be subordinate to a purchase order raised against it, so the PO can vary individual terms. It would be rare, and indicative of careless drafting, if two clauses within the same set of Ts & Cs were in conflict; however if this did occur the default position would usually be that the later numbered clause prevails - there would need to be overwhelming evidence that this would be manifestly absurd if the opposite were to apply.
I am unaware of Virginia Contract interpretation.Notwithstanding this fact, Ideally,a clarification on contradictory contract provision needs to be sought by the bidder with the Employer through a pre-bid query to remove ambiguity and bring clarity through review/amendment at pre-bid stage itself.In case of overlook,the issue can be got clarified through an amendment to contract before award/signing of contract.Any further ignorance, post award of contract, will have consequential cost to the benefit of either party to the contract.