Finite Math: Midterm Exam

Berkeley College-Spring-2013 MATH 210- Finite Math-Prof. Seaton

Name: February 11, 2013

PRACTICE PROBLEMS FOR MIDTERM EXAM-ANSWERS 1) The total cost to produce 10 calculators is $100. The variable cost per calculator is $4. (a) Find the fixed cost 10 4 4 10 40 60

100

(b) What is the cost function? 4 60

2) An insurance company claims that its monthly revenue in dollars is given by R(x) = 125x and its monthly cost is: C(x) = 100x + 5000, where x represents the number of policies in thousands. Find the break-even point R(x) = C(x) 125x = 100x + 5000 25x = 5000 x = 200

3) The total annual enrollment ( in millions) in U.S elementary schools for the
P (2500)  R(2500)  C (2500) P (2500)  12(2500)  5(2500)  14, 000 P (2500)  (12  5)(2500)  14, 000 P (2500)  7(2500)  14, 000 P (2500)  17500  14, 000 P (2500)  3500

4

d) How many units should the firm produce in order to realize a minimum monthly profit of $7,000?

R( x)  C ( x)  7000 12 x  (5 x  14000)  7000

12 x  5 x  14000  7000 7 x  14000  7000 7 x  21000 x  3000

9) A stone is thrown upward from the ground. The height above the ground (in feet) at any time t is given by the function: h(t )  16t 2  1000t , where t is the time in seconds. (a) When does the stone reach its highest point? (b) What is the stone’s maximum height from the ground? (c) At what time does the stone hit the ground? (a) a  16, b  1000 b 1000 1000 125 t     31.25 2a 2  16  32 4
(b)

h  31.25   16(31.25)2  1000(31.25) h  31.25   15625  31250 h(31.25)  15625

(c)The stone will hit the ground when h = 0 h(t )  16t 2  1000t 0  16t 2  1000t 0  4t  4t  250 

4t  0 & 4t  250  0 250 125 t  0&t    62.5 4 2