Johnson Lube is interested in producing and selling an industrial line of oil filters. Market research indicates that wholesale customers are currently willing to pay $$8$ for similar filters, and that the company could sell $80,000$ units per year at that price.

Required:

a$.$ If Johnson Lube requires a $19$ percent return on sales, what is its target cost for the proposed industrial line of filters?

b$.$ Assume that market research reveals several of Johnson Lube$$s direct competitors are likely to lower the wholesale price of similar filters to $$7$ per unit. To remain competitive, what will the company$$s target cost have to be to maintain a $19$ percent return on sales?

c$.$ At a wholesale price of $$7,$ Johnson Lube estimates that it can sell $83,400$ industrial filters per year instead of $80,000$ units. Assuming its target costs are attainable, how much more or less profit per year will the company earn at the $$7$ wholesale price compared to the initial wholesale price estimate of $$8?$