A competitor, Beta Electronics, sets up an identical factory (same fixed and variable costs) producing y thousand chips per month. (a) (1 mark) Find P(x, y) and Q(x, y), the profit functions for the Alpha and Beta factories, respec- tively. Note that the price the chips can be sold at corresponds to the demand of the combined production q = x+y. (b) (2 marks) If the two companies agree to produce the same amount = y what is the maximum profit they can each achieve and the corresponding production x? (c) (1 mark) Explain in words (one sentence) why the combined profit of the two companies is lower than the maximum profit of one producer from question #2. q(p) = 20e P. Note that there is still demand q> 0 even for very large prices p (some consumers need these chips no matter the cost). The chip factory has fixed costs of $1,000 per month and each chip costs $1 to manufacture.