Supply and Demand and Optimal Selling Essay

1176 Words Apr 22nd, 2013 5 Pages
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Math 116 Review 1
1. Suppose that the total cost of manufacturing q units of a certain product is C  q  thousand dollars, where
C  q   q3  30q2  500q  200

a) Find the total cost and the average cost of producing 10 units. b) Find the cost of producing the 10th unit.

2. Let f  x   4 x 2  3x  2 , evaluate and simplify the difference quotient

f  x  h  f  x , where h  0 . h

3. The average scores of incoming students at an eastern liberal arts college in the SAT mathematics examination have been declining at a constant rate in recent years. In 2000, the average SAT score was 605. The score is decreasing at a rate of 6 points per year. Form a linear function of time for the average SAT score. Let
…show more content…
Use the limit of the difference quotient to find the slope of the tangent line to 18. Find the derivative of the function. Make sure all answers have whole number exponents. a) y  x  9 x  2
3 2

at x=-1.

b) y  4 x
3

2

 2 x 5  5 x 3  3x c) y  x
M116v12.doc

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19. A ball is thrown upward from the top of a 160-foot cliff. The initial velocity of the ball is 48 feet per second, which implies that the position function is s  t   16t 2  125t  200 , where the time t is measured in seconds. Find the height, the velocity, and the acceleration of the ball when t  3

Answers:
1. (a) C 10  $3,200,000 , AC 10  $320,000 2. DQ  8x  4h  3 4. (a) 5. (a) 15 feet (b) Optimal price  $21 (b) 25 seconds (b) Cost of the 10th unit  $201,000 3. (c) Number of sets/week  30 sets (c) maximum height = 9,985 feet (b) V  7  $12,250 (b) Maximum profit  $144,000

6. C  x   12,000  0.03x , R  x   0.07 x , P  x   0.04 x  12,000 , Break-even point: x  300,000 copies 7. (a) V  t   2,250t  28,000 8. (a) Optimal selling price/lamp  $41 9. (a) xe  10 units, pe  $35 (b) (c) Market shortage: 0  x  10 Market surplus: 10. a) S(x)= x  10

b)

inches

c) 11.45 inches

x3 11. V  x   4 x  Cubic meters 3

12. (a) A  x   7.5  13. 34 16. (a) 2 17. 18. a) y'  3x 2 

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