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Problem Two companies are producing widgets. It costs the first company q dollars to produce q, widgets and the second company 0.75q dollars to produce q, widgets. If a total of q widgets are produced, consumers will pay 300 - q dollars for each widget. If the two companies want to collude in an attempt to maximize the sum of their profits, how many widgets should each company produce? (The model for this type of problem is called a collusive duopoly model.) A B C D E F G I 1 J K L 4 5 1. Problem #53 (30 points) 6 Collusive duopoly 7 8 9 Cost for each firm to produce q units is of form aq, where Company 1 Company 2 1 2 10 a 0.75 11 b 2 12 13 14 Unit price if q units are produced is c-dq, where 300 d 1 15 16 17 18 Company 1 Company 2 Total Production for each firm Units produced 19 0 20 21 23 24 25 Cost for Company 1 Cost for Company 2 Total cost Total revenue Total profit Answer Key Cell C25 = 15750