In the past, Alpha Corporation has not performed incoming quality control inspections but has taken the word of its vendors. However, Alpha has been having some unsatisfactory experience recently with the quality of purchased items and wants to set up sampling plans for the receiving department to use.

For a particular component, X$,$ Alpha has a lot tolerance percentage defective of $40$ percent. Zenon Corporation, from which Alpha purchases this component, has an acceptable quality level in its production facility of $15$ percent for component X$.$ Alpha has a consumer's risk of $10$ percent, and Zenon has a producer's risk of $5$ percent.

When a shipment of Product X is received from Zenon Corporation, what sample size should the receiving department test? and What is the allowable number of defects in order to accept the shipment?