basic 11 math questions needs to be answered by friday(12/12/13-10am!!

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Berkeley College-Prof. Seaton Name: Math 210-Fall 2013 November 22, 2013 MIDTERM EXAM PLEASE SHOW ALL WORK WHERE POSSIBLE. PARTIAL CREDIT WILL BE GIVEN WHERE APPLICABLE 1) The total cost to produce 10 calculators is $100. The variable cost per calculator is $6.

(a) Find the fixed cost (5 points)

(b) What is the cost function? (3 points)

2) The cost and revenue functions of a department is given respectively as: ( ) 125 3000 & ( ) 140C x x R x x . (a) What is their break-even point? (5 points)

(b) What would be the cost and revenue if 40 units were sold? (4 points)

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3) The total annual enrollment (in millions) in U.S elementary schools for the years 1975- 1996 is given by the model: 2( ) 0.058 1.162 50.604E x x x (a) When was the enrollment the lowest? (5 points)

(b) What was the enrollment to the nearest tenth of a million? (4 points)

4) Solve for x: Solve for m: 5 2 5

3 4 3 m m

(8 points)

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5) The average cost of water rate is given by the function 3 2( ) 0.01 0.5 1.25 0.35C t t t t , where C(t) is measured in dollars/year and t = 0 represents the year 2000. What will be the average cost in the year 2010? (5 points)

6. Greg Tobin sells bottled water. He has found that the average amount of time he spends with each customer is related to his weekly sales volume by the function: 2( ) 60f x x x . Here x represents the number of minutes per customer and f(x) is the number of cases sold per week.

(a) How many minutes does Greg have to spend with a customer to sell the maximum number of cases?

(3 points)

(b) What was the maximum number of cases sold for this customer? (2 points)

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(c) What is the maximum number of minutes he can spend with a customer to make some profit? (4 points)

7) Find the quadratic function whose vertex is (3, 2) and passes through the point (6, 11) (8 points)

8. Puritron, a manufacturer of water filters, has a monthly fixed cost of $20,000, a production cost of $20 per unit, and a selling price of $30 per unit. (a) Find the cost function C(x) for a water filter. (3 points)

(b) Find the revenue function R(x) for a water filter. (3 points)

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(c) Find the profit function P(x) for a water filter. (4 points) (d)What profit is gained or lost is 1500 water filters are sold? (3 points)

9. A company manufactures its products at a cost of $5 per unit and sells them for $12 per unit. If the firm’s fixed cost is $7,000 per month.

a) Determine the firm’s break-even point. (4 points)

b) What is the loss sustained by the firm if only 800 units are produced and sold each month? (3 points)

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c) What is the profit if 1,500 units are produced and sold each month? (3 points)

d) How many units should the firm produce in order to realize a minimum monthly profit of $14,000? (5 points)

10) The function: 2( ) 0.0534 0337 0.969N x x x gives the number of active-duty military personnel in the United States Army (in millions) for the years 1965-1972, where x = 0 corresponds to 1965, x = 1 corresponds to 1966, and so on. What was the army’s personnel strength level in the year 1968? (5 points)

11) An object is thrown upward from the ground with an initial velocity of 80 ft/second. The height after t seconds is given by the function: 2( ) 80 16 16 5h t t t t t , (a) When does the object reach its maximum height? (3 points)

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(b) What is the maximum height of this object? (3 points) (c) At what time does the stone hit the ground? (5 points)