# Supply and Demand and Optimal Selling Essay

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…*

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