Mathematics Exercise Questions on Supply and Demand, and Optimal Selling
Page 1 of 4
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 t=0 for 2000.
4. The owner of a toy store can obtain a popular board game at a cost of $15 per set. She estimates that if each set sells for p dollars, then sets will be sold each week. a) Express the owner’s weekly profit as a function of selling price p. b) Estimate the optimal selling price. c) How many sets will be sold each week at that optimal price?
5. A missile is projected vertically from an underground bunker in such a way that t seconds after lunch, it is s feet above the ground, where s t 16t 2 800t 15 a) How deep is the bunker? b) Determine when the missile is at its highest point. c) What is the missile maximum height?
M116v12.doc
Page 2 of 4
6. George runs a copying service, and he charges 7 cents per copy. The cost of the copy machine is $8000, the cost of a life time maintenance service is $4000, and the cost of making a single copy is 3 cents. Find the cost function, the revenue function, the profit function, and the break-even point.
7. A manufacturer buys $28,000 worth of machinery that depreciates linearly so that its trade-in value after 12 years will be $1,000 a) Express the value of the machinery as a function of its age. b) Compute the value of the machinery after 7 years.
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 t=0 for 2000.
4. The owner of a toy store can obtain a popular board game at a cost of $15 per set. She estimates that if each set sells for p dollars, then sets will be sold each week. a) Express the owner’s weekly profit as a function of selling price p. b) Estimate the optimal selling price. c) How many sets will be sold each week at that optimal price?
5. A missile is projected vertically from an underground bunker in such a way that t seconds after lunch, it is s feet above the ground, where s t 16t 2 800t 15 a) How deep is the bunker? b) Determine when the missile is at its highest point. c) What is the missile maximum height?
M116v12.doc
Page 2 of 4
6. George runs a copying service, and he charges 7 cents per copy. The cost of the copy machine is $8000, the cost of a life time maintenance service is $4000, and the cost of making a single copy is 3 cents. Find the cost function, the revenue function, the profit function, and the break-even point.
7. A manufacturer buys $28,000 worth of machinery that depreciates linearly so that its trade-in value after 12 years will be $1,000 a) Express the value of the machinery as a function of its age. b) Compute the value of the machinery after 7 years.