3. (30 points) A new assembly line for mass production of shoes is under investigation by a shoe manufacturer. The new line costs $500,000 and operating costs are expected to be $150,000 per year. Planned annual production is 8,000 pairs and the price of a pair of shoes is $40. The line's service life is considered to be five years, and the MV of the line five years later is expected to be 30% of the original investment. Assume a 10% annual interest rate for the base case. a) (10 pts) How many shoes should the manufacturer produce to reach a break-even point? b) (5 pts) Does manufacturer make any profit under the given production plan? Explain. c) (15 pts) Perform a sensitivity analysis with respect to the interest rate for +20% in terms of present worth. Comment on your results briefly