Week_10_solutions

Week_10_solutions - 1 WEEK 10 - SOLUTIONS TUTORIAL...

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1 WEEK 10 - SOLUTIONS TUTORIAL QUESTIONS 1. HPW 13.3, Problem 70, p.587 Answer:  A x A x e A e e A x xe A e x g xe A e x g A x A U A x A x A U A x A U 2 2 2 2 2 2 0 2 2 0 2 0 ) ( ' ' ) ( ' If A x 0 , the graphic is concave down. If A x , the graphic is concave up. 2. HPW 14.1, Problem 46, p.692 Answer: (a) 32 1 65 6500 40,000 2 at 100 460,000 Pq q q qP   (b) P ( q + dq ) is approximately P ( q ) + dP 2 3 98 (100 ( 2)) (100) ( 130 6500) 2 443,000 PP P q q d q  3. From June 3. (From June 1998 exam) A company has a single product which sells for a price of $(50-0.01 q) per unit, where q is the quantity produced and sold. It has fixed costs of $35,000 per month and variable costs of $ 2 1 20 q per unit. How many units should it sell per month to maximise profit. (Check the second order conditions for a maximum.) Answer: Profit is 1 2 3 2 2 50 0.01 20 35,000 30 qq q q q  2 1 2 3 02 . 0 30 q q dq d .
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2 Let 2 q a then 41 . 91 2 82 . 107 75 0 2 3 02 . 0 30 2 a a a (ignore the negative root) and 72 . 8355 q . Maximum
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Week_10_solutions - 1 WEEK 10 - SOLUTIONS TUTORIAL...

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