Three alternative designs have been created by Snakisco engineers for a new machine that spreads cheese between the crackers in a Snakisco snack. Each machine design has unique total costs (fixed and variable) based on the annual production rate of boxes of these crackers. The costs for the three designs are given (where x is the annual production rate of boxes of cheese crackers).

You are asked to do the following.
(a) Mathematically determine which of the machine designs would be recommended for different levels of annual production of boxes of snack crackers. Management is interested in the production interval of 0-150,000 boxes of crackers per year. Over what production volume would each design (A or B or C) be chosen?
(b) Depict your solution from part (a) graphically, putting x per year on the horizontal axis and $ on the vertical axis, so that management can see more easily the following:
i. Accurate total cost lines for each alternative (show line, slopes, and line equations).
ii. Any relevant breakeven, or crossover points in terms of costs between the alternatives.
iii. Ranges of annual production where each alternative is preferred.
iv. Clearly label your axes and include a title for the graph.

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Variable Cost (S/x) DesignFixed Cost $100,000 350,000 600,000 20.5x 10.5x 8.0x