Majda Lux must select a supplier for a plastic bottle and proprietary dispenser for its new hair shampoo.

Three suppliers have placed bids; at Majda's request, all bids are for a shipping quantity of $20,000$ bottles

with annual requirements of $40,000$ units. Majda's factory operates $250$ days a year. The first table shows

each supplier's price, estimated annual freight costs, and current lead times; management has added

estimates for holding costs and administrative oversight costs for each supplier.

Beyond costs, however, Majda has three other criteria considered important in the selection of a supplier.

The second table shows all the criteria, their weights, and the scores for all of them except total costs,

where a score of $1$ indicates "poor" and $10$ indicates "superior." Because all three suppliers have done

business with Majda Lux before, management will assign a score of $"10"$ to the supplier with the lowest

total annual cost, a score of $"8\mathrm{.}5"$ for the next lowest cost, and a score of $"7\mathrm{.}0"$ for the worst cost of the

three.

a$.$ Which of the three suppliers will provide the lowest annual cost to Majda Lux?

b$.$ Given Majda's criteria and weighting system, which supplier should Majda award the contract to$?$