MATH 111 – EXAM I Hints and Answers
Version Alpha
Autumn 2008
1. (a) (4 points) HINT: Price per item is the same as average revenue. Average revenue at
q= 3 hundred Items is the slope of the diagonal line through the TR graph at 3.
ANSWER: approximately $86.67 per Item
(b) (4 points) HINT: You’re looking for the marginal revenue at q= 4 hundred Items. Draw
the secant line through the T R graph at q= 4.00 and q= 4.01 and compute its slope.
ANSWER: approximately $53.33
(c) (2 points) NOTE: There was a typo on this exam. The fixed costs should have been
140 hundred dollars.
ANSWER: The T C graph is a line parallel to the V C graph with “y”-intercept 140.
(d) (4 points) ANSWER: Since T C is linear, every time you produce one more Item, your
total cost will increase by the same amount (that amount being the slope of the T C
graph: approximately 23.70). So, the graph of marginal cost will be a horizontal line
with height 23.70.
(e) (4 points) HINT: Profit (the vertical distance between TR and T C ) is largest at about
q= 6 hundred Items.
ANSWER: Maximum profit is approximately 120 hundred dollars or $12000.
2. (4 points each)
(a) HINT: The smallest value of MC is the “y”-coordinate of the lowest point on the M C
graph.
ANSWER: $2 per Thing
(b) HINT: The breakeven price is the “y”-coordinate of the point of intersection of MC and
AC.
ANSWER: approximately $6.55 per Thing
(c) HINT: Average cost at 7 Things is approximately $8.30 per Thing and AC(7) = T C (7)
7.
ANSWER: approximately $58.10
(d) HINT: Draw the graph of MR: a horizontal line with height 5.50. Profit is maximized
at the smallest whole number quantity at which MR becomes less than or equal
to MC.
ANSWER: 11 Things
3. (a) (6 points – 3 points each)
i. ANSWER: A(5) −A(0)
ii. ANSWER: B(t+h)−B(t)
h
(b) (4 points) HINT: Draw a reference line with slope 2. Slide your reference line up until it
intersects the graph of Bat its “y”-intercept and find another point at which it intersects
the Bgraph.
ANSWER: approximately t= 0.7 or t= 5.2
(c) (4 points) HINT: Find a time at which the vertical gap between the two graphs is 3 and
the Bgraph is above the Agraph.
ANSWER: approximately t= 8.25
(d) (2 points) ANSWER: iii