The Bathtub Division of Bramble Plumbing Corporation has recently approached the Faucet Division with a proposal. The Bathtub Division would like to make a special "ivory" tub with gold$-$plated fixtures for the company's $50-$year anniversary. It would make only $6,400$ of these units. It would like the Faycet Division to make the fixtures and provide them to the Bathtub Division at a transfer price of $$200.$ If sold externally, the estimated thit variable cost would be $$184.$ However, by selling internally, the Faucet Division would save $$9$ per unit on variable selling expenses. The Faucet Division is currently operating at full capacity. Its standard unit sells for $$64$ per unit and has variable costs of $$47.$

Compute the minimum transfer price that the Faucet Division should be willing to accept.

Minimum transfer price $

Should they accept this offer?

They this offer.