Final Review 3

# Final Review 3 - -5 e 2 x where x is the number of cases of...

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MATH 1331 Spring 2006 Final Exam Review #3 Rules for Integration Z x n dx = x n +1 n + 1 + C Z ( f ( x )) n f 0 ( x ) dx = f ( x ) n +1 n + 1 + C Z e x dx = e x + C Z 1 x dx = ln | x | + C Z b a f 0 ( x ) dx = f ( b ) - f ( a ) Consumers’ Surplus is Z x 0 0 [ D ( x ) - p 0 ] dx Producers’ Surplus is Z x 0 0 [ p 0 - S ( x )] dx CHAPTER 5 and 6: MAXIMIZATION and INTEGRATION 1. A farmer wishes to enclose a rectangular ﬁeld of area 400 square feet using an existing wall as one of the sides. The cost of the fence for the other three sides is \$5 per foot. Find the dimensions of the rectangular ﬁeld that will minimize the cost. 2. A theater owner charges \$5 per ticket and sells 250 tickets. By checking other theaters, the owner decides that for every dollar she raises the ticket price, she will lose 10 customers. What should she charge to maximize revenue? 3. Find the cost function for an adhesive tape manufacturer if the marginal cost is given by 100

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Unformatted text preview: -5 e 2 x where x is the number of cases of tape produced and the ﬁxed costs are \$100. 4. Suppose the rate of change of spending is given by P ( t ) =-10 t 2 (4 t 3 + 11) 2 + 100. Find the amount of spending during the ﬁrst two years. 5. Z x (3-x 2 ) 7 dx 6. Z 2 √ x + 1 dx 7. Suppose the rate of sales of an item is given by-t 3 + 3 t 2 + 15 , where t is the number of weeks after an advertising campaign has begun. How many items were sold during the third week? 8. In industry, the demand equation is given to be D ( x ) = 50-x 2 , and the supply equation is given to be S ( x ) = 5 x . (a) Find the equilibrium point. (b) Find the consumer surplus. (c) Find the producer surplus...
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Final Review 3 - -5 e 2 x where x is the number of cases of...

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