Benson Chairs, Incorporated makes two types of chairs. Model Diamond is a high$-$end product designed for professional offices.

Model Gold is an economical product designed for family use. Jane Silva, the president, is worried about cut$-$throat price competition

in the chairs market. Her company suffered a loss last quarter, an unprecedented event in its history. The company's accountant

prepared the following cost data for Ms$.$ Silva:

The market price for office chairs comparable to Model Diamond is $$122$ and to Model Gold is $$70.$

Required

a$.$ Compute the cost per unit for both products.

b$.$ Dan Barker, the chief engineer, told Ms$.$ Silva that the company is currently making $144$ units of Model Diamond per batch and $199$

units of Model Gold per batch. He suggests doubling the batch sizes to cut the number of setups in half, thereby reducing the setup

cost by $50$ percent. Compute the cost per unit for each product if Ms$.$ Silva adopts his suggestion.

$($For all requirements, round intermediate calculations and final answers to $2$ decimal places.$)$