Here is all the information they have given us:

This is a first year calculus course

Too answer question four we need information from question 2 and question 3

4. (*vvk) Alpha Electronics keeps their production xed at a: from the previous question. Beta Electronics realizes that they can increase prots by changing their production y. Note that this question will require a calculator or other computational tools for numerical answers. (a) (2 marks) Write Q(y) in this situation and calculate Q'(y). (b) (2 marks) Find the appropriate critical point for Q using Newton's method. Show the iteration formula, your initial estimate of the root of Q', and the next three iterates. Also show the critical point value that you believe is accurate to four decimal places. (c) (2 marks) Compute the optimal prot for Beta Electronics in this scenario. What is the prot for Alpha Electronics now (still producing at a: from the previous question)? 2. (**7(7() Dr. Bob sets up a new company, Alpha Electronics, producing specialized but low tech computer chips. The demand q in thousands of chips per month is related to the price p in dollars by q(p) = 2061). Note that there is still demand q > 0 even for very large prices 19 (some consumers need these chips no matter the cost). The chip factory has xed costs of $1,000 per month and each chip costs $1 to manufacture. (a) (1 mark) Find the inverse of the demand curve, the function p(q). (b) (2 marks) Find the prot function P($) in thousands of dollars per month Where :r is the production of the factory in thousands per month matching demand ((1 = x) (c) (2 marks) Find the maximum prot per month and the corresponding production x. Give a short justication of how you know this is the maximum. 3. (* * *jf'z) A competitor, Beta Electronics, sets up an identical factory (same xed and variable costs) producing y thousand chips per month. (a) (1 mark) Find 13(33, y) and Q(;E,y), the prot 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 = a: + y. (b) (2 marks) If the two companies agree to produce the same amount a: = y what is the maximum prot they can each achieve and the corresponding production 3:? (c) (1 mark) Explain in words (one sentence) why the combined prot of the two companies is lower than the maximum prot of one producer from question #2