Williams Inc. 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 56,500 parts in the coming year. While the demand for Williamss 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 industrys current downturn. Total Costs Variable manufacturing $ 4,667,000 Variable selling and administrative 842,650 Facility-level fixed overhead 2,332,875 Fixed selling and administrative 662,495 Batch-level fixed overhead 347,000 Total investment in product line 22,337,000 Expected sales (units) 56,500 Required: 1. Determine the price for the part using a markup of 35% of full manufacturing cost. 2. Determine the price for the part using a markup of 24% of full life-cycle cost. 3. Determine the price for the part using a desired gross margin percentage to sales of 45%. 4. Determine the price for the part using a desired life-cycle cost margin percentage to sales of 29%. 5. Determine the price for the part using a desired before-tax return on investment of 12%. 6. Determine the total contribution margin and total operating profit for each of the methods in requirements 1 through 5.