MA110 Lecture 69: 14.7 Maximum and Minimum values + Fermat's theorem (2 variable) + second derivative test (2 variable)

Virtually every item sold in a store has a 12-digit UPC barcodewhich is scanned at the checkout counter. The first 11 digits of aUPC number d1d2d3 ? ? ? d11d12 identify the manufacturer andproduct. The last digit d12 is a check digit which is chosen sothat 3d1+d2+3d3+d4+3d5+d6+3d7+d8+3d9+d10+3d11+d12 =0 pmod10q.

If the congruence does not hold, an error has been made and theitem must be scanned again, or the UPC code entered by hand. Whichof the following UPC numbers were scanned incorrectly?

Please see the attached image for the full question.

Please also provide the answer in a handwritten response thathas been scanned or with a photo rather than typed. Highest pointswill be given to most detailed answers.