Please show your working and explain the reasoning for your answer.

NitroFizz makes beer can widgets. The dedicated engineers working in the NitroFizz research and development team have created three prototypes that they believe will be equally effective in enhancing the head effect in canned beer. The costs for the three designs are: Design Fixed Cost Variable Cost ($/unit) ($/month) A $37,000 0.264 B $69,000 0.142 C $120,000 0.193 Management is interested in the production interval of 0 - 1 million widgets per month. (a) Determine the production volume over which each design would be chosen, if it is chosen at all. (b) For a production volume of 500,000 widgets, calculate the average unit cost and the marginal cost. (C) Assuming that widgets sell for 50 cents each, calculate the monthly breakeven quantity. What is the contribution margin at the breakeven production volume