Download Spring 2000

Math 128b, Section 3
Second Examination
Spring 2000
Name_____________________________________
Please show all your work on these pages.
Formulas are on the last page. You may use a calculator.
Question
1
2
3
4
5
6
7
Total
Points
8
8
8
20
24
24
8
100
Score
1
1. Manufacturing a good has a fixed cost of $600 thousand plus a variable cost of $200 per unit.
(a) What is the total cost to produce 55 units?
(b) Find a formula giving the total cost in dollars as a function of q, the number of units
produced.
2. The demand function for a product is given by D(q) = 400 – 0.03q2. Prices are in dollars and
quantity is in units of the item.
(a) At what price are 10 units demanded?
(b) Above what price are no units demanded?
3. Values of a function f(x) are given in the following table. Estimate the derivative when x = 21;
that is, estimate f ( 21) .
x
20.7
20.8
20.9
21.0
21.1
21.2
21.3
f(x)
12.62
12.49
12.37
12.25
12.12
12.00
11.88
4. Consider the following points: (1.8, 4.2), (3.1, 6.9), (3.7, 7.9), (4.6, 10.1).
2
(a) Plot the points on the axes below.
11
10
9
8
y
7
6
5
4
3
2
1
0
0
1
2
3
4
5
x
(b) Roughly sketch a straight line that fits the data well.
(c) Using the line you have drawn, predict the value of y when x = 0. Mark this point on your
graph.
(d) What is the approximate slope of your line?
(e) What is the approximate equation of your line?
5. The following graph shows revenue and cost as a function of quantity sold.
3
(a) Which is the revenue graph and which is the cost graph?
(b) For approximately what quantities does the company make a profit?
(c) Estimate the maximum revenue.
(d) Approximately what quantity of the good should be sold to generate this maximum revenue?
(e) Estimate the maximum profit.
(f) Approximately what quantity of the good should be sold to generate this maximum profit?
Revenue & Cost Functions
$200
(M's)
$150
$100
$50
$0
0
200
400
600
800
1,000
1,200
1,400
1,600
q (K's)
6. The following graph shows marginal revenue (the curve) and marginal cost (the lines) as a
function of the quantity produced.
4
(a) The marginal cost graph consists of three horizontal line segments. What does this tell you in
practical business terms?
(b) The graph shows that MR(400) = 200. What are the units of the 400? Of the 200?
(c) What does the fact that MR(400) = 200 tell you in practical business terms?
(d) At approximately what value(s) of q is (are) revenue a maximum?
$(M's) per unit of q
(e) At approximately what value(s) of q is (are) profit a maximum?
$300
$250
$200
$150
$100
$50
$0
-$50 0
-$100
-$150
200
400
600
800
q (K's)
5
1,000
1,200
1,400
1,600
7. Let f(x) = 3x. Estimate f (2) using h = 0.1. Give your answer accurate to two decimal places.
Formulas
P(q) = R(q)  C(q)
R(q) = qD(q)
Slope 
Rise
Run
MP(q) = MR(q)  MC(q)
f ( x ) 
6
f ( x  h)  f ( x  h)
2h