Williams Incorporated produces a single product, a part used in the manufacture of automobile transmissions. Known for its

quality and performance, the part is sold to luxury auto manufacturers around the world. Because this is a quality product,

Williams has some flexibility in pricing the part. The firm calculates the price using a variety of pricing methods and then

chooses the final price based on that information and other strategic information. A summary of the key cost information

follows. Williams expects to manufacture and sell $52,500$ parts in the coming year. While the demand for Williams's part has

been growing in the past $2$ years, management is not only aware of the cyclical nature of the automobile industry, but also

concerned about market share and profits during the industry's current downturn.

Required:

Determine the price for the part using a markup of $35\%$ of full manufacturing cost.

Determine the price for the part using a markup of $20\%$ of full life$-$cycle cost.

Determine the price for the part using a desired gross margin percentage to sales of $35\%.$

Determine the price for the part using a desired life$-$cycle cost margin percentage to sales of $25\%.$

Determine the price for the part using a desired before$-$tax return on investment of $15\%.$

Determine the total contribution margin and total operating profit for each of the methods in requirements $1$ through $5.$