Please provide step by step so I can understand the process and use this for future reference.

1) Mary Williams, owner of Williams Products, is evaluating whether to introduce a new product line. After thinking through the production process and the costs of raw materials and new equipment. Williams estimates the variable costs of each unit produced and sold at $6 and the fixed costs per year at $60,000

a. If the selling price is set at $18 each, how many units must be produced and sold for Williams to break even? Use both graphic and algebraic approach to get your answer.

b. Williams forecasts sales of 10,000 units for the first year if the selling price is set at $16.00 each. What would be the total contribution to profits from this new product during the first year?

c. If the selling price is set at $12.50, Williams forecasts that first-year sales would increase to 15,000 units. Which pricing strategy ($14.00 or $12.50) would result in the greater total contribution to profits?

d. What other considerations would be crucial to the final decision about making and marketing the new product?

2) A product at the Jennings Company has enjoyed reasonable sales volumes, but its contributions to profits were disappointing. Last year, 17,500 units were produced and sold. The selling price is $22 per unit, the variable cost is $18 per unit, and Fix cost is $80,000.

a. What is the break-even quantity for this product? Use both graphic and algebraic approach to get your answer.

b. If sales were not expected to increase, by how much would Jennings have to reduce their variables cost to break even?

c. Jennings believes that $1 reduction in price will increase sales by 50 percent. Is this enough for Jennings to break even? If not, by how much would sales have to increase?

d. Jennings is considering ways to either stimulate sales volume or decrease variable costs. Management believes that either sales can be increased by 30 percent or that variable cost can be reduced to 85 percent of its current level. Which alternative leads to higher contributions to profits, assuming that each is equally costly to implement? (Hint: Calculate profits for both alternatives and identify the one having the greatest profits.)

e. What is the percent change in the per-unit profit contribution generated by each alternative in part b?

3) An interactive television service that costs $10 per month to provide can be sold on the information highway for $15 per client per month. If a service are includes a potential of 15,000 customers, what is the most a company could spend on annual fixed cost to acquire and maintain the equipment?

4) A restaurant is considering adding a fresh book trout to its menu. Customers would have the choice of catching their own trout from a simulated mountain stream or simply asking the waiter to net the trout for them. Operating the stream would require $10,600 in fix costs per year. Variable costs are estimated to be $6.70 per trout. The firm wants to break even if 800 trout dinners are sold per year. What should be the price of the new item?

5) Spartan Castings must implement a manufacturing process that reduces the amount of particulates emitted into the atmosphere. Two processes have been identified that provide the same level of particulate reduction. The first process is expected to incur $350,000 of fixed cost and add $50 of variable cost to each casting Spartan produces. The second process has fixed costs of $150,000 and adds $90 of variable cost per casting.

a. What is the break-even quantity beyond which the first process is more attractive?

b. What is the difference in total cost if the quantity produced is 10,000?