You are sourcing an assembly component from three suppliers: Supplier X$,$ Y$,$ and Z$.$

In the last year, Supplier $x$ delivered $$300,000$ worth of the components, and there were $12$ instances of late delivery. Supplier $Y$ delivered $$150,000$ worth of the components, and there were $300$ defective items that had to be reworked. Supplier Z delivered $$200,000$ worth of the components, and there was $1$ occurrence where the entire shipment had to be returned to the supplier.

The average cost for each type of failure event is as follows:

Late delivery: $$2,000($per occurrence$)$

Rework: $$50($per item$)$

Return to supplier: $$10,000($per occurrence$)$

Below is the unit component price from each supplier:

Supplier X: $$500($per component$)$

Supplier Y: $$510($per component$)$

Supplier Z: $$520($per component$)$

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