Lake University entered into a contract with Carpenter Co. by which Carpenter agreed to complete the construction of a new dormitory no later than March 1. Lake University also entered into a separate contract with Plumber Co., which agreed to install all the plumbing fixtures in the dormitory after the building was constructed. Because Carpenter did not finish the construction until December, the plumbing installation was delayed by more than eight months. Plumber sued Carpenter for breach of contract alleging that Carpenter’s failure to complete the building by March 1 caused Plumber to incur damages of $10,000. Is Plumber entitled to sue Carpenter as a third-party beneficiary of the Lake-Carpenter contract? Explain.